Patients cannot have:\r\n* Active central nervous system or meningeal involvement by lymphoma; patients with a history of central nervous system (CNS) or meningeal involvement must be in a documented remission by cerebrospinal fluid (CSF) evaluation and contrast-enhanced magnetic resonance imaging (MRI) imaging for at least days prior to registration\r\n* Evidence of myelodysplasia or cytogenetic abnormality indicative of myelodysplasia on any bone marrow biopsy prior to initiation of therapy\r\n* A known bleeding diathesis\r\n* Requirement for warfarin or similar vitamin K antagonists; these drugs are prohibited days prior to the first treatment and throughout the trial\r\n* History of stroke or intracranial hemorrhage =< months before treatment\r\n* Currently active, clinically significant hepatic impairment (Child-Pugh class B or C according to the Child Pugh classification\r\n* History of allergic reactions attributed to compounds of similar chemical or biologic composition to ibrutinib or other agents used in study\r\n* Serologic status reflecting active hepatitis B or C infection; patients that are positive for hepatitis B core antibody, hepatitis B surface antigen (HBsAg), or hepatitis C antibody must have a negative polymerase chain reaction (PCR) prior to enrollment; (PCR positive patients will be excluded) Positive serologic or polymerase chain reaction (PCR) test results for acute or chronic hepatitis B virus (HBV) infection Known history of hepatitis B or hepatitis C infection or known positive test for hepatitis B surface antigen, hepatitis B core antigen, or hepatitis C polymerase chain reaction (PCR) Patients seropositive or PCR positive for the human immunodeficiency virus (HIV). Patients with evidence of Hepatitis B or Hepatitis C PCR positivity Active hepatitis C infection, defined as presence of hepatitis C virus (HCV) antibody; active hepatitis B infection is allowed, defined as presence of hepatitis B virus (HBV) surface antigen by polymerase chain reaction (PCR) if subject is agreeable to antiviral therapy with entecavir or lamivudine (must have virologic control of hepatitis B); subjects will require HBV PCR monitoring per institutional standard Known to be seropositive for hepatitis B (defined by a positive test for hepatitis B surface antigen [HBsAg]). Participants with resolved infection (participants who are positive for antibodies to hepatitis B core antigen [antiHBc] and/or antibodies to hepatitis B surface antigen [antiHBs]) must be screened using real-time polymerase chain reaction (PCR) measurement of hepatitis B virus (HBV) DNA levels . Those who are polymerase chain reaction (PCR) positive will be excluded Subjects with known active hepatitis B (HBV) or hepatitis C (HCV) infection as defined by the following (hepatitis screening studies are required):\r\n* Positive test for hepatitis B surface antigen\r\n* Positive test for hepatitis C antibody and/ or hepatitis C quantitative viral load (Note: subjects with a positive hepatitis C antibody and negative quantitative hepatitis C polymerase chain reaction [PCR] viral load are eligible) Presence of fungal, bacterial, viral, or other infection that is uncontrolled or requiring IV antimicrobials for management; simple urinary tract infection (UTI) and uncomplicated bacterial pharyngitis are permitted if responding to active treatment; ongoing infection with human immunodeficiency virus (HIV) or hepatitis B (hepatitis B surface antigen [HBsAg] positive) or hepatitis C virus (anti hepatitis C virus [HCV] positive); a history of hepatitis B or hepatitis C is permitted if the viral load is undetectable per quantitative polymerase chain reaction (PCR) and/or nucleic acid testing Known seropositive for or active viral infection with human immunodeficiency virus (HIV), hepatitis B virus (HBV) or hepatitis C virus (HCV); patients who are seropositive because of hepatitis B virus vaccine are eligible; patients who are positive for hepatitis B core antibody or hepatitis B surface antigen must have a negative polymerase chain reaction (PCR) result before enrollment; those who are PCR positive will be excluded Known history of hepatitis B or hepatitis C infection or known positive test for hepatitis B surface antigen, hepatitis B core antigen, or hepatitis C polymerase chain reaction (PCR) Active infection with hepatitis C virus (HCV) or hepatitis B virus (HBV)\r\n* Subjects who are positive for hepatitis B core antibody, hepatitis B surface antigen, hepatitis C antibody, must have a negative polymerase chain reaction (PCR) result for the respective disease before enrollment; those who are PCR positive will be excluded Known history of human immunodeficiency virus (HIV) or active with hepatitis C virus (HCV) or hepatitis B virus (HBV); subjects who are positive for hepatitis B core antibody or hepatitis B surface antigen must have a negative polymerase chain reaction (PCR) result before enrollment; those who are PCR positive will be excluded Patients with a history of hepatitis B (surface antigen or core antibody positive and polymerase chain reaction [PCR] positive) must take lamivudine or equivalent drug during study therapy and for one year after completion of all therapy; patients on intravenous immunoglobulin (IVIG) who are core antibody positive but PCR negative are not mandated to take prophylaxis Known active hepatitis B (defined as most recent serum polymerase chain reaction [PCR] or hepatitis B surface antigen positive) or active hepatitis C (note, hepatitis C in sustained virologic response defined as negative ribonucleic acid [RNA] PCR at least weeks after any therapy is permitted) Active human immunodeficiency virus (HIV) or hepatitis C virus (HCV) or hepatitis B virus (HBV); subjects who have an undetectable HIV viral load with CD >= and are on highly active antiretroviral therapy (HAART) medication are allowed; subjects who are positive for hepatitis B core antibody or hepatitis B surface antigen must have a negative polymerase chain reaction (PCR) result before enrollment; those who are PCR positive will be excluded; patients who have had hepatitis C but have finished treatment and are PCR negative will be allowed; (testing to be done only in patients suspected of having infections or exposures) Serologic status reflecting active hepatitis B or C infection. Patients that are positive for hepatitis B core antibody, hepatitis B surface antigen (HBsAg), or hepatitis C antibody must have a negative polymerase chain reaction (PCR) prior to enrollment. (PCR positive patients will be excluded.) Negative hepatitis B surface antigen (HBsAg) and negative hepatitis B core (HBc) antibody or undetectable hepatitis B (HBV) deoxyribonucleic acid (DNA) by quantitative polymerase chain reaction (PCR) testing. Evidence of active hepatitis B infection, based on positive surface antigen or hepatitis B deoxyribonucleic acid (DNA) polymerase chain reaction (PCR), or active hepatitis C infection; patients who are hepatitis B core antibody positive must take prophylaxis with lamivudine or equivalent and be willing to undergo monthly hepatitis B DNA PCR testing Exclusion of hepatitis infection based on the following results and/or criteria: Positive for hepatitis B surface antigen (HBsAg) (indicative of chronic hepatitis B or recent acute hepatitis B); Negative HBsAg and positive for hepatitis B core antibody: hepatitis B virus DNA by polymerase chain reaction (PCR) is necessary. Detectable hepatitis B virus DNA suggests occult hepatitis B Documented human immunodeficiency virus (HIV) infection or positive serology, active bacterial infections, serologic or polymerase chain reaction (PCR) evidence for active or chronic hepatitis B or hepatitis C Subjects with a positive Hepatitis B surface antigen and/or antihepatitis B core antibody. Subjects with a negative polymerase chain reaction (PCR) assay are permitted with appropriate antiviral prophylaxis. Patients must be hepatitis C virus (HCV) negative (by quantitative PCR [qPCR]) and hepatitis B virus core antibody (HBcAb) negative (no prior hepatitis B infection) Serologic status reflecting active hepatitis B or C infection; patients who are hepatitis B core antibody positive and who are antigen negative, will need to have a negative polymerase chain reaction (PCR) result prior to enrollment; those who are hepatitis B antigen positive or PCR positive, will be excluded Active hepatitis C infection with a positive PCR; subjects who are hepatitis C antibody positive and PCR negative may be eligible; in these cases the subjects will be monitored via hepatitis C virus (HCV) PCR throughout the study Uncontrolled intercurrent illness including, but not limited to the following that may limit interpretation of results or that could increase risk to the patient at the discretion of the investigator:\r\n* Active autoimmune disease that has required systemic treatment in the past years (i.e., with use of disease modifying agents, corticosteroids or immunosuppressive drugs); NOTE: Replacement therapy (e.g., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc.) is not considered a form of systemic treatment\r\n* History of (non-infectious) pneumonitis that required steroids, evidence of interstitial lung disease or active, non-infectious pneumonitis\r\n* Hepatitis B virus surface antigen or hepatitis B core antibody positive\r\n* Active hepatitis C infection; NOTE: Subjects who are hepatitis C antibody positive will need to have a negative polymerase chain reaction (PCR) result before enrollment; those with a positive PCR for hepatitis C are excluded\r\n* Uncontrolled and/or symptomatic thyroid disease\r\n* Active graft-versus (vs)-host disease (GVHD) requiring treatment or any history of >= grade II acute GVHD\r\n* Seizure activity within the past weeks\r\n* Known mental or physical illness that would interfere with cooperation with the requirements of the trial or confound the results or interpretation of the results of the trial and, in the opinion of the treating investigator, would make the patient inappropriate for entry into the study Positive test for hepatitis C antibody (patients with documented clearance of hepatitis C by polymerase chain reaction [PCR] following treatment will be permitted) Known history of human immunodeficiency virus (HIV) or active with hepatitis C virus (HCV) or hepatitis B virus (HBV). Subjects who are positive for hepatitis B core antibody, hepatitis B surface antigen, or hepatitis C antibody must have a negative polymerase chain reaction (PCR) result before enrollment. Those who are PCR positive will be excluded. Viral hepatitis:\r\n* Patients with active hepatitis B defined by hepatitis B surface antigen positivity or core antibody positivity in the presence of detectable serum hepatitis B deoxyribonucleic acid (DNA) viremia are not eligible for this study\r\n* Patients with a positive hepatitis B core antibody but with negative hepatitis B DNA maybe considered for participation, but must agree to receive appropriate anti-hepatitis B viral therapy suppression therapy while on obinutuzumab and have hepatitis B DNA monitored every weeks with real-time polymerase chain reaction (PCR) by the treating physician; these patients should be referred to a hepatologist or gastroenterologist for appropriate monitoring and management\r\n* Hepatitis C: patients with positive hepatitis C serology unless hepatitis C virus (HCV) ribonucleic acid (RNA) is confirmed negative by PCR Active hepatitis B infection as documented by positive hepatitis B polymerase chain reaction (PCR) assay Human immunodeficiency virus (HIV)-positive patients regardless of treatment are excluded; patients with evidence of active hepatitis B and hepatitis C infection with positive real time polymerase chain reaction (qPCR) are also excluded but patients with prior exposure to hepatitis B or C with negative qPCR are allowed Active hepatitis C, defined by the detection of hepatitis C ribonucleic acid (RNA) in plasma by polymerase chain reaction (PCR) Immunocompromised patients, patients with known history of testing positive for human immunodeficiency virus (HIV) or known acquired immunodeficiency syndrome (AIDS) and currently receiving antiretroviral therapy, active hepatitis B virus surface antigen (HBV sAg+), active hepatitis C (if antibody [Ab]+ then polymerase chain reaction [PCR]+) indicating acute or chronic infection Known history of human immunodeficiency virus (HIV) or active with hepatitis C virus (HCV) or hepatitis B virus (HBV); subjects who are positive for hepatitis B core antibody or hepatitis B surface antigen must have a negative polymerase chain reaction (PCR) result before enrollment; those who are PCR positive will be excluded Known history of infection with human immunodeficiency virus (HIV) or hepatitis B (HBsAg positive) or hepatitis C virus (anti-HCV positive). If there is a positive history of treated hepatitis B or hepatitis C, the viral load must be undetectable per quantitative polymerase chain reaction (PCR) and/or nucleic acid testing. Known to be seropositive for hepatitis B (defined by a positive test for hepatitis B surface antigen [HBsAg]). Participants with resolved infection (ie, participants who are positive for antibodies to hepatitis B core antigen [antiHBc] and/or antibodies to hepatitis B surface antigen [antiHBs]) must be screened using real-time polymerase chain reaction (PCR) measurement of hepatitis B virus (HBV) deoxyribonucleic acid (DNA) levels. Those who are PCR positive will be excluded Positive study for Hepatitis B surface antigen or Hepatitis B or C confirmed by polymerase chain reaction (PCR) Active hepatitis C infection; subjects positive hepatitis C antibody test are eligible if polymerase chain reaction (PCR) is negative for hepatitis C viral DNA Active with hepatitis C virus (HCV) or hepatitis B virus (HBV), subjects who are positive for hepatitis B core antibody or hepatitis B surface antigen must have a negative polymerase chain reaction (PCR) result before enrollment, those who are PCR positive will be excluded; subjects who have an undetectable human immunodeficiency virus (HIV) viral load with CD >= and are on highly active antiretroviral therapy (HAART) medication are allowed; previously treated hepatitis C patients are also allowed; as there is potential for hepatic toxicity with nivolumab or nivolumab/ipilimumab combinations, drugs with a predisposition to hepatoxicity should be used with caution in patients treated with nivolumab-containing regimen Active human immunodeficiency virus (HIV) or hepatitis C virus (HCV) or hepatitis B virus (HBV); subjects who have an undetectable HIV viral load with CD >= and are on highly active antiretroviral therapy (HAART) medication are allowed; subjects who are positive for hepatitis B core antibody or hepatitis B surface antigen must have a negative polymerase chain reaction (PCR) result before enrollment; those who are PCR positive will be excluded; patients who have had hepatitis C but have finished treatment and are PCR negative will be allowed; (testing to be done only in patients suspected of having infections or exposures) Active infection with human immunodeficiency virus (HIV), hepatitis C virus (HCV) or hepatitis B virus (HBV); subjects who are positive for hepatitis B core antibody, hepatitis B surface antigen, or hepatitis C antibody must have a negative polymerase chain reaction (PCR) result before enrollment; those who are PCR positive will be excluded; subjects with HIV must have a CD count at or above the institutional lower limit of normal and not taking prohibited CYPA strong inhibitors Evidence of active hepatitis B infection, based on positive surface antigen or hepatitis B deoxyribonucleic acid (DNA) polymerase chain reaction (PCR), or active hepatitis C infection; patients who are hepatitis B core antibody positive must take prophylaxis with lamivudine or equivalent and be willing to undergo monthly hepatitis B DNA PCR testing Known human immunodeficiency virus (HIV), hepatitis C virus (HCV) or hepatitis B virus (HBV) infection; subjects who are positive for hepatitis B core antibody or hepatitis B surface antigen must have a negative polymerase chain reaction (PCR) result before enrollment; those who are PCR positive will be excluded Known history of human immunodeficiency virus (HIV) or active with hepatitis C virus (HCV) or hepatitis B virus (HBV); subjects who are positive for hepatitis B core antibody or hepatitis B surface antigen must have a negative polymerase chain reaction (PCR) result before enrollment; those who are PCR positive will be excluded Presence of hepatitis B surface antigen (HBsAg) or positive hepatitis C antibody test result at screening or within months prior to first dose of study treatment. Subjects with positive Hepatitis C antibody due to prior resolved disease can be enrolled only if a confirmatory negative Hepatitis C RNA polymerase chain reaction (PCR) is obtained. Active hepatitis C, defined by the detectable hepatitis C ribonucleic acid (RNA) in plasma by polymerase chain reaction (PCR) Known history of human immunodeficiency virus (HIV) or active with hepatitis C virus (HCV) or hepatitis B virus (HBV); subjects who are positive for hepatitis B core antibody or hepatitis B surface antigen must have a negative polymerase chain reaction (PCR) result before enrollment; those who are PCR positive will be excluded; subjects who have an undetectable human immunodeficiency virus (HIV) viral load with CD >= and are on highly active antiretroviral therapy (HAART) medication are allowed Presence of human immunodeficiency virus (HIV) (antibody [Ab] positivity), or active hepatitis A, B or C infection (active infection will be defined as hepatitis A immunoglobulin M [IgM] Ab positivity, hepatitis B surface Ag positivity, or hepatitis C polymerase chain reaction [PCR] positivity, respectively) Current or chronic hepatitis B or C infection, or known seropositivity for human immunodeficiency virus (HIV); subjects who are positive for hepatitis B or C core antibody or hepatitis B or C surface antigen must have a negative polymerase chain reaction (PCR) result before enrollment; those who are PCR positive will be excluded; Note: Patients who are receiving intravenous immunoglobulins may become seropositive for hepatitis B antibodies; these patients are allowed on the study without additional testing Patients known to be positive for hepatitis B surface antigen expression or with active hepatitis C infection (positive by polymerase chain reaction or on antiviral therapy for hepatitis C within the last months); patients with history of human immunodeficiency virus (HIV) disease are also excluded from the study Acute or chronic hepatitis B or hepatitis C infection (requires negative test for clinically suspected hepatitis B or hepatitis C infection)\r\n* Evidence of hepatitis B -\r\n** Positive hepatitis B virus (HBV) surface antigen (indicative for chronic hepatitis B or recent acute hepatitis B)\r\n** Negative HBV surface antigen but positive HBV total core antibody (indicative for resolved hepatitis B infection or occult hepatitis B) and detectable copies of HBV deoxyribonucleic acid (DNA) by polymerase chain reaction (PCR) (detectable HBV DNA copies suggest occult hepatitis B)\r\n* Evidence of hepatitis C - \r\n** Positive hepatitis C virus (HCV) antibody and positive HCV ribonucleic acid (RNA) by PCR (undetectable RNA copies suggest past and resolved hepatitis C infection) Active hepatitis B or hepatitis C (virus detectable by polymerase chain reaction [PCR]) Known history of human immunodeficiency virus (HIV) or active with hepatitis C virus (HCV) or hepatitis B virus (HBV); patients who are positive for hepatitis B core antibody or hepatitis B surface antigen must have a negative polymerase chain reaction (PCR) result before enrollment; those who are PCR positive will be excluded Exclusion of hepatitis infection based on the following results and/or criteria: Positive for hepatitis B surface antigen (HBsAg) (indicative of chronic hepatitis B or recent acute hepatitis B). Negative HBsAg and positive for hepatitis B core antibody: Assay for hepatitis B virus DNA by polymerase chain reaction (PCR) is necessary. Detectable hepatitis B virus DNA suggests occult hepatitis B. Positive Hepatitis C virus antibody (HCVAb): Assay for hepatitis C virus RNA by PCR is necessary. Detectable hepatitis C virus RNA suggests chronic hepatitis C. Untreated HIV or active hepatitis C detectable by polymerase chain reaction (PCR), or chronic hepatitis B (patients positive for hepatitis B core antibody who are receiving intravenous immunoglobulin (IVIG) are eligible if hepatitis B [HepB] polymerase chain reaction [PCR] is negative). Active human immunodeficiency virus (HIV) or hepatitis C virus (HCV) or hepatitis B virus (HBV); subjects who have an undetectable HIV viral load with CD > and are on highly active antiretroviral therapy (HAART) medication are allowed; subjects who are positive for hepatitis B core antibody or hepatitis B surface antigen must have a negative polymerase chain reaction (PCR) result before enrollment; those who are PCR positive will be excluded; patients who have had hepatitis C but have finished treatment and are PCR negative will be allowed (testing to be done only in patients suspected of having infections or exposures) REGISTRATION TO TREATMENT (STEP ): Patients with a known positive test for hepatitis C virus ribonucleic acid (hepatitis C virus [HCV] antibody) indicating acute or chronic infection might be enrolled if the viral load by polymerase chain reaction (PCR) is undetectable with/without active treatment For high risk and very high risk CLL-IPI (Arms A and B) only:\r\n* Any of the following:\r\n** Pregnant persons\r\n** Nursing persons\r\n** Persons of childbearing potential who are unwilling to employ highly effective contraception\r\n* Serologic status reflecting active hepatitis B or C infection\r\n** NOTE: Subjects with hepatitis B core antibody positive who are surface antigen negative or who are hepatitis C antibody positive will need to have a negative polymerase chain reaction (PCR) result before randomization; those who are hepatitis B surface antigen positive or hepatitis B PCR positive and those who are hepatitis C PCR positive will be excluded\r\n* History of stroke or intracranial hemorrhage within months before randomization\r\n* History of bleeding diathesis (e.g. hemophilia, von Willebrand disease)\r\n* Requires or receiving anticoagulation with warfarin or equivalent vitamin K antagonists (e.g. phenprocoumon) within days of first dose of study drug and while on study\r\n* Requires treatment with a strong CYPA inducer\r\n* Requires treatment with proton-pump inhibitors (e.g. omeprazole, esomeprazole, lansoprazole, dexlansoprazole, rabeprazole, or pantoprazole)\r\n* Presence of a gastrointestinal ulcer diagnosed by endoscopy within months before screening\r\n* History of confirmed progressive multifocal leukoencephalopathy (PML)\r\n* Received a vaccination with a live vaccine ? days prior to randomization Known history of hepatitis B (defined as hepatitis B surface antigen [HBsAg] reactive) or known active hepatitis C virus (by polymerase chain reaction [PCR]) Active infection with human immunodeficiency virus (HIV), hepatitis C virus (HCV) or hepatitis B virus (HBV); subjects who are positive for hepatitis B core antibody, hepatitis B surface antigen, or hepatitis C antibody must have a negative polymerase chain reaction (PCR) result before enrollment; those who are PCR positive will be excluded; subjects with HIV must have a CD count at or above the institutional lower limit of normal and not taking prohibited CYPA strong inhibitors Patients with positive hepatitis B surface antigen (HepBsAg), positive hepatitis total core antibody with negative HBsAG, or detectable hepatitis C virus ribonucleic acid (RNA) by a polymerase-chain reaction (PCR) assay (screening is generally done by hepatitis C antibody (HepCAb), followed by hepatitis C virus RNA by PCR if HepCAb is positive) Immunocompromised patients, patients with known history of testing positive for human immunodeficiency virus (HIV) or known acquired immunodeficiency syndrome (AIDS) and currently receiving antiretroviral therapy, patients with a prior history of known or suspected autoimmune disease, active hepatitis B virus surface antigen (HBV sAg+), active Hepatitis C (if antibody [Ab]+ then polymerase chain reaction [PCR]+) indicating acute or chronic infection, and/or history of interstitial lung disease Positive hepatitis B surface antigen (HepBsAg) (indicative of chronic hepatitis B), positive hepatitis total core antibody with negative HBsAG (suggestive of occult hepatitis B), or detectable hepatitis C virus RNA by a polymerase-chain reaction (PCR) assay (indicative of active hepatitis C screening is generally done by hepatitis C antibody [HepCAb], followed by hepatitis C virus RNA by PCR if HepCAb is positive); subjects with hepatitis B virus suppressed on therapy, and previously treated/eradicated hepatitis C virus are eligible for study Patients with active history of any acute or chronic hepatitis, as evidenced by a positive test for hepatitis B (e.g., hepatitis B surface antigen [HBsAg] reactive) or a positive test for qualitative hepatitis C viral load by polymerase chain reaction (e.g., hepatitis C virus [HCV] ribonucleic acid [RNA] [qualitative] is detected)\r\n* Subjects with positive hepatitis C antibody and negative quantitative hepatitis C by polymerase chain reaction are eligible\r\n* Subjects with a history of resolved hepatitis A virus infection are eligible Known serologic status reflecting active hepatitis B or C infection; patients that are hepatitis B core antibody positive, but antigen negative, will need a negative polymerase chain reaction (PCR) prior to enrollment (NOTE: hepatitis B antigen or PCR positive patients will be excluded) Serologic status reflecting active hepatitis B or C infection; patients that are positive for hepatitis B core antibody, hepatitis B surface antigen (HBsAg), or hepatitis C antibody must have a negative polymerase chain reaction (PCR) prior to enrollment (PCR positive patients will be excluded) Patients are excluded if they are hepatitis B surface antigen (sAg), hepatitis B (Hep B) core antibody (cAb), or hepatitis C (Hep C) positive; patients with hepatitis B cAB positive and hepatitis B polymerase chain reaction (PCR) negative are eligible if they started prophylactic treatment prior to registration to trial Serologic status reflecting active hepatitis B or C infection; patients that are positive for hepatitis B core antibody, hepatitis B surface antigen (HBsAg), or hepatitis C antibody must have a negative polymerase chain reaction (PCR) prior to enrollment; (PCR positive patients will be excluded) Negative hepatitis B surface antigen (HBsAg) and negative hepatitis B core (HBc) antibody or undetectable hepatitis B virus (HBV) deoxyribonucleic acid (DNA) by quantitative polymerase chain reaction (PCR) testing Known history of human immunodeficiency virus (HIV) or active infection with hepatitis C virus (HCV) or hepatitis B virus (HBV); patients who are positive for hepatitis B core antibody or hepatitis B surface antigen must have a negative polymerase chain reaction (PCR) result before enrollment; those who are PCR positive will be excluded Known history of human immunodeficiency virus (HIV) or active with hepatitis C virus (HCV) or hepatitis B virus (HBV); patients who are positive for hepatitis B core antibody or hepatitis B surface antigen must have a negative polymerase chain reaction (PCR) result before enrollment; those who are PCR positive will be excluded Positive hepatitis B surface antigen (HepBsAg) (indicative of chronic hepatitis B), positive hepatitis total core antibody with negative HBsAG (suggestive of occult hepatitis B), or detectable hepatitis C virus ribonucleic acid (RNA) by a polymerase-chain reaction (PCR) assay (indicative of active hepatitis C screening is generally done by hepatitis C antibody [HepCAb], followed by hepatitis C virus RNA by PCR if HepCAb is positive) For patients with positive hepatitis B core antibody or surface antigen, hepatitis B polymerase chain reaction (PCR) must be negative and prophylaxis with entecavir or equivalent is required Known history of hepatitis B or C infection or known positive test for hepatitis B surface antigen or core antigen, or hepatitis C polymerase chain reaction (PCR) Subjects with serologic status reflecting active viral hepatitis B or C infection are not eligible\r\n* Subjects who are hepatitis B core antibody positive but antigen negative will need negative polymerase chain reaction (PCR) prior to enrollment; hepatitis B surface antigen positive or PCR positive patients will be excluded\r\n* Subjects who are hepatitis C antibody positive will need negative PCR prior to enrollment; patients with positive hepatitis C will be excluded Presence of hepatitis B surface antigen (HBsAg) or positive hepatitis C antibody test result at screening or within months prior to first dose of study treatment. History of known HIV infection. NOTE: Subjects with positive Hepatitis C antibody due to prior resolved disease can be enrolled only if a confirmatory negative Hepatitis C ribonucleic acid (RNA) polymerase chain reaction (PCR) is obtained. Known history of human immunodeficiency virus (HIV), active infection with hepatitis B virus (HBV), and/or hepatitis C virus (HCV); subjects who are positive for hepatitis B core antibody or hepatitis B surface antigen must have a negative polymerase chain reaction (PCR) result before enrollment; those who are PCR positive will be excluded Patients known to be positive for hepatitis B surface antigen expression or with active hepatitis C infection (positive by polymerase chain reaction or on antiviral therapy for hepatitis C within the last months) or with a history of human immunodeficiency virus (HIV) disease Known seropositive for or active viral infection with human immunodeficiency virus (HIV), hepatitis B virus (HBV) or hepatitis C virus (HCV); patients who are seropositive because of hepatitis B virus vaccine are eligible; patients who are positive for hepatitis B core antibody or hepatitis B surface antigen must have a negative polymerase chain reaction (PCR) result before enrollment; those who are PCR positive will be excluded Subjects with serologic status reflecting active viral hepatitis B or C infection are not eligible; subjects that are hepatitis B core antibody positive but antigen negative will need negative polymerase chain reaction (PCR) prior to enrollment; PCR-positive patients will be excluded Patients must not have any of the following conditions:\r\n* Congestive heart failure or New York Heart Association Functional Classification III or IV congestive heart failure\r\n* History of myocardial infarction, unstable angina, or acute coronary syndrome within months prior to registration\r\n* Recent infections requiring systemic treatment; need to have completed anti-biotic therapy > days before the first dose of study drug\r\n* Cerebral vascular accident or intracranial bleed within the last months\r\n* Infection with known chronic, active hepatitis C\r\n* Serologic status reflecting active hepatitis B or C infection; patients that are positive for hepatitis B core antibody, hepatitis B surface antigen (HBsAg), or hepatitis C antibody must have a negative polymerase chain reaction (PCR) prior to enrollment (PCR positive patients will be excluded) Known history of human immunodeficiency virus or active hepatitis C virus (HCV; ribonucleic acid [RNA] polymerase chain reaction [PCR]-positive) or active hepatitis B virus (HBV; DNA PCR-positive) infection or any uncontrolled active systemic infection requiring intravenous antibiotics Presence of hepatitis B surface antigen (HBsAg), positive hepatitis C antibody test result within months prior to first dose of study treatment. Subjects with positive Hepatitis C antibody due to prior exposure can be enrolled, only if a confirmatory negative Hepatitis C RNA polymerase chain reaction (PCR) test is obtained. Active hepatitis B or C infection\r\n* Patients with hepatitis B virus (HBV) core antibody positive, but HBV polymerase chain reaction (PCR) negative are eligible if they are on medication for suppression of HBV reactivation\r\n* Patients with hepatitis C virus (HCV) antibody positive, but PCR negative are eligible Serologic status reflecting active hepatitis B or C infection; patients that are positive for hepatitis B core antibody, hepatitis B surface antigen (HBsAG), or hepatitis C antibody, must have a negative polymerase chain reaction (PCR) prior to enrollment; (PCR positive patients will be excluded) Serologic status reflecting active hepatitis B or C infection; patients that are hepatitis B core antibody, hepatitis B surface antigen (HBsAg) or hepatitis C antibody must have a negative polymerase chain reaction (PCR) prior to enrollment; PCR positive patients will be excluded DONOR: Donors must not be newly seropositive for hepatitis B core antibody since the original HCT; donors with prior evidence of hepatitis B core antibody positivity will have a polymerase chain reaction (PCR) test done to evaluate for hepatitis B infection; donors with a positive hepatitis (Hep) B PCR test will be excluded Subjects who have current active hepatic (hepatitis B-virus surface antigen [HbsAg], hepatitis B-virus core antibody [HbcAb], and positive viral load by polymerase chain reaction [PCR]) or biliary disease (with exception of patients with Gilbert's syndrome, asymptomatic gallstones, liver metastases or stable chronic liver disease per investigator assessment) (consult with a physician experienced in care and management of subjects with hepatitis B to manage/treat subjects who are anti-HBc positive) Active hepatitis b virus (positive hepatitis b surface antigen) or active hepatitis c virus (measurable viral ribonucleic acid [RNA] load with polymerase chain reaction) infection Patients with known positive hepatitis B surface antigen (HepBsAg) (indicative of chronic hepatitis B), positive hepatitis total core antibody with negative HBsAG (suggestive of occult hepatitis B), or detectable hepatitis C virus RNA by a polymerase-chain reaction (PCR) assay (indicative of active hepatitis C screening is generally done by hepatitis C antibody (HepCAb), followed by hepatitis C virus RNA by PCR if HepCAb is positive) Known history of infection with human immunodeficiency virus (HIV) or history of active or chronic infection with hepatitis C virus (HCV) or hepatitis B virus (HBV), or any uncontrolled active systemic infection; hepatitis B surface antigen must be confirmed negative within one year before enrollment; subjects who are positive for hepatitis B core antibody or hepatitis B surface antigen must have a negative polymerase chain reaction (PCR) result before enrollment; those who are PCR positive will be excluded Known history of human immunodeficiency virus (HIV) or active with hepatitis C virus (HCV) or hepatitis B virus (HBV); subjects who are positive for hepatitis B core antibody or hepatitis B surface antigen must have a negative polymerase chain reaction (PCR) result before enrollment; those who are PCR positive will be excluded Active hepatitis B infection as documented by positive hepatitis B polymerase chain reaction (PCR) assay Known history of human immunodeficiency virus (HIV) or active with hepatitis C virus (HCV) or hepatitis B virus (HBV). Subjects who are positive for hepatitis B core antibody or hepatitis B surface antigen must have a negative polymerase chain reaction (PCR) result before enrollment. Those who are PCR positive will be excluded. Serologic status reflecting active hepatitis B or C infection; patients that are hepatitis B core antibody positive but antigen negative will need a negative polymerase chain reaction (PCR) prior to enrollment; (hepatitis B antigen or PCR positive patients will be excluded;) (this may not be a necessary exclusion for an ibrutinib monotherapy protocol) Serologic status reflecting active hepatitis B or C infection; patients that are positive for hepatitis B core antibody, hepatitis B surface antigen (HBsAg), or hepatitis C antibody will need a negative polymerase chain reaction (PCR) prior to enrollment (PCR positive patients will be excluded); hepatitis C antibody positive patients are eligible if PCR is negative Subjects meeting the following criteria will be excluded from enrollment in the pre-phase arm of the study, but may be included in the GA only arm\r\n* Contraindication to use rituximab or prednisone including:\r\n** Uncontrolled diabetes mellitus\r\n** Systemic fungal infection\r\n** Evidence of active hepatitis B infection (i.e. patients testing positive for hepatitis B surface antigen or viral deoxyribonucleic acid [DNA] by polymerase chain reaction [PCR] analysis) will be excluded; patients with evidence of past infection without active viremia (i.e. positive hepatitis B DNA PCR) will be treated with entecavir as per institutional guidelines and may be included in the study\r\n** History of any serious adverse reaction to either a corticosteroid or rituximab not including rituximab infusion reactions =< grade Active hepatitis C infection; patients positive hepatitis C antibody test are eligible if polymerase chain reaction (PCR) is negative for hepatitis C viral DNA Known history of hepatitis B or C infection or known positive test for hepatitis B surface antigen or core antigen, or hepatitis C polymerase chain reaction (PCR) Known history of human immunodeficiency virus (HIV) or active with hepatitis C virus (HCV) or hepatitis B virus (HBV); subjects who are positive for hepatitis B core antibody or hepatitis B surface antigen must have a negative polymerase chain reaction (PCR) result before enrollment; those who are PCR positive will be excluded Known history of human immunodeficiency virus (HIV) or active hepatitis C virus (HCV) or hepatitis B virus (HBV); patients who are positive for hepatitis B core antibody or hepatitis B surface antigen must have a negative polymerase chain reaction (PCR) result before enrollment; those who are PCR positive will be excluded EXCLUSION CRITERIA FOR ENROLLMENT (PRE-TRANSPLANT): Known history of human immunodeficiency virus (HIV) or active hepatitis C virus (HCV) or hepatitis B virus (HBV) infection; subjects who are positive for hepatitis B core antibody or hepatitis B surface antigen must have a negative polymerase chain reaction (PCR) result before enrollment; those who are PCR positive will be excluded Evidence of any active uncontrolled infection (bacterial, viral or fungal) or evidence of natural exposure to hepatitis B, hepatitis C or human immunodeficiency virus (HIV) without demonstration of polymerase chain reaction (PCR) negativity for said virus; vaccination to hepatitis B is not an exclusion criterion Subjects with positive test for hepatitis C (HCV) infection are excluded regardless of viral load. If hepatitis C antibody test is positive, a confirmatory polymerase chain reaction (PCR) or Recombinant immunoblot assay (RIBA) test should be performed. If the PCR or RIBA test is negative, subject is eligible for this trial Active hepatitis C infection; subjects positive hepatitis C antibody test are eligible if polymerase chain reaction (PCR) is negative for hepatitis C viral DNA History of human immunodeficiency virus (HIV) or active hepatitis C virus (HCV) or hepatitis B virus (HBV); patients who are positive for hepatitis B core antibody or hepatitis B surface antigen must have a negative polymerase chain reaction (PCR) result before enrollment; those who are PCR positive will be excluded