Ages =< 50 years of age with chronic lymphocytic leukemia (CLL) T-cell large granular lymphocytic leukemia Richter transformation of chronic lymphocytic leukemia/small lymphocytic lymphoma Lymphoma fulfilling the following criteria: Chemotherapy-sensitive (at least stable disease lymphomas that have failed at least 1 prior regimen of multi-agent chemotherapy and are INELIGIBLE for an autologous transplant. Patients with chronic lymphocytic leukemia (CLL) are not eligible regardless of disease status. Group B: CD19+ B cell chronic lymphocytic leukemia (CLL) or non-Hodgkin lymphoma (NHL) undergoing allogeneic HSCT Patient must have diagnosis of CLL that meets published 2008 International Workshop on Chronic Lymphocytic Leukemia (IWCLL) National Cancer Institute–sponsored Working Group (NCI-WG) criteria Must have histologically or flow cytometry confirmed diagnosis of B-cell chronic lymphocytic leukemia/small lymphocytic lymphoma (B-CLL/SLL) according to National Cancer Institute Working Group (NCI-WG) 1996 guidelines; the malignant B cells must co-express CD5 with CD19 or CD20; patients who lack CD23 expression on their leukemia cells should be examined for (and found NOT to have) either t(11;14) or cyclin D1 overexpression, to rule out mantle cell lymphoma; patients with CLL who have progressed on prior ibrutinib therapy will be eligible; patients with B-cell prolymphocytic leukemia and patients with Richter’s transformation of CLL/SLL are NOT eligible Diagnosis of chronic lymphocytic leukemia (CLL) meeting criteria established in the International Workshop on Chronic Lymphocytic Leukemia (IWCLL) 2008 criteria for the diagnosis and treatment of CLL Ages =< 50 years with chronic lymphocytic leukemia (CLL) No treatment indication according to IWCLL/NCI-WG (International Working Group in Chronic Lymphocytic Leukemia/National Cancer Institute-Working Group) 2008 criteria. Diagnosis of chronic lymphocytic leukemia (CLL)/small lymphocytic lymphoma (SLL) that meets IWCLL diagnostic criteria. Diagnosis of chronic lymphocytic leukemia (CLL) or small lymphocytic leukemia (SLL) meeting International Workshop on Chronic Lymphocytic Leukemia (IWCLL)/National Cancer Institute (NCI)-Working Group (WG) criteria, and relapsed after or refractory to at least 1 prior treatment Chronic lymphocytic leukemia (CLL)/small lymphocytic lymphoma (SLL), or high-grade lymphomas (Burkitt’s lymphoma/lymphoblastic lymphoma) Small lymphocytic lymphoma Patients with chemo-sensitive chronic lymphocytic leukemia (CLL)/small lymphocytic lymphoma (SLL) with persistent or recurrent disease after fludarabine-based regimens with < 25% involvement by CLL/SLL cells Chronic lymphocytic leukemia with high risk disease as defined by the European Society for Blood and Marrow Transplantation (EBMT) consensus criteria Small lymphocytic lymphoma (SLL), or chronic lymphocytic leukemia (CLL) with progressive disease following a minimum of two lines of standard therapy Diagnosis of B-cell chronic lymphocytic leukemia (B-CLL), confirmed by flow cytometry and as per the criteria outlined by the IWCLL/Hallek December 2008 Documented CD19+ chronic lymphocytic leukemia (CLL) or small lymphocytic lymphoma (SLL) Small lymphocytic lymphoma with absolute lymphocyte count <5x10E9/L at study entry Histologically confirmed diagnosis of follicular lymphoma grade 3b or transformed disease, or chronic lymphocytic leukemia. Histologically or cytologically confirmed Hodgkin and all NHL subtypes excluding Burkitt, chronic lymphocytic leukemia (CLL) and lymphoblastic lymphoma that is considered to have relapsed or to be refractory to primary chemotherapy Clinically significant and ongoing immune suppression including, but not limited to, systemic immunosuppressive agents such as cyclosporine or corticosteroids, chronic lymphocytic leukemia (CLL), uncontrolled human immunodeficiency virus (HIV) infection, or solid organ transplantation Participants with a diagnosis of chronic lymphocytic leukemia (CLL) or small lymphocytic lymphoma (SLL). Must have a confirmed diagnosis of CLL defined by 2008 International Workshop on Chronic Lymphocytic Leukemia (iwCLL) criteria Patients with chronic lymphocytic leukemia/small lymphocytic lymphoma Small lymphocytic lymphoma(SLL) with absolute lymphocyte count <5x10*9/L at study entry Histologically confirmed diagnosis of follicular lymphoma grade 3b or transformed disease, or chronic lymphocytic leukemia Indication for treatment as defined by the International Workshop in Chronic Lymphocytic Leukemia (IWCLL) Guidelines Have documented chronic lymphocytic leukemia (CLL)/small lymphocytic lymphoma (SLL) according to National Cancer Institute (NCI) criteria Confirmed B-cell non-Hodgkin lymphoma (NHL), chronic lymphocytic leukemia (CLL)/small lymphocytic lymphoma (SLL), and other B-cell lymphoproliferative disorders as approved by the Medical Monitor or Study Chair Patients with small lymphocytic lymphoma (SLL)/chronic lymphocytic leukemia (CLL) are excluded during the phase I portion of the study Histologically confirmed chronic lymphocytic leukemia (CLL)/small lymphocytic lymphoma (SLL) Patients with active chronic lymphocytic leukemia (CLL) disease requiring urgent chemotherapy Low-grade non-Hodgkin lymphoma (including small lymphocytic lymphoma [SLL] and chronic lymphocytic leukemia [CLL]) or plasma cell neoplasm that has progressed after at least two prior therapies (excluding single agent rituximab and single agent steroids), or in the case of lymphoma undergone histologic conversion; patients with transformed lymphomas must have stable disease or better Diagnosis of B-CLL, confirmed by flow cytometric analysis and as per the criteria outlined by the International Workshop on Chronic Lymphocytic Leukemia (IWCLL)/Hallek December 2008 Diagnosis of chronic lymphocytic leukemia with no history of previous treatments with monoclonal antibodies or chemotherapy. Confirmed diagnosis of B-cell Chronic Lymphocytic Leukemia Diagnosis of active CLL or SLL that meets at least 1 of the International Workshop on Chronic Lymphocytic Leukemia (IWCLL) 2008 criteria for requiring treatment Diagnosis of chronic lymphocytic leukemia (CLL) meeting criteria established in the World Health Organization (WHO) classification of hematologic disorders or International Workshop on Chronic Lymphocytic Leukemia (IWCLL) Patients with a history of CD19+ lymphoid malignancy defined as acute lymphoblastic leukemia (ALL), non-Hodgkin lymphoma (NHL), small lymphocytic lymphoma (SLL), or chronic lymphocytic leukemia (CLL) with active disease defined by presence of > 5% malignant blasts in bone marrow and/or peripheral blood, and/or minimal residual disease by flow cytometry or molecular analysis for fusion proteins, and/or positive imaging for extramedullary disease. Patients must have measurable disease at time of study treatment. Histological confirmation of relapsed/refractory B-cell NHL, CD20+ \r\n* NOTE: patients with small lymphocytic lymphoma (SLL) are eligible however patients with chronic lymphocytic leukemia (CLL) are not eligible\r\n* Waldenstrom macroglobulinemia patients are not eligible; aggressive lymphoma patients who are transplant eligible must have undergone a transplant\r\n* The biopsy confirming relapse can be up to 24 weeks prior to registration as long as there is no intervening therapy Known immunosuppressive disease, for example HIV infection or history of bone marrow transplant or chronic lymphocytic leukemia (CLL). FOR PATIENTS WITH CHRONIC LYMPHOCYTIC LEUKEMIA (CLL): Histologically confirmed diagnosis of recurrent B-cell non-Hodgkin's lymphoma (any\n histology by WHO criteria) or recurrent chronic lymphocytic leukemia (by NCI\n criteria) (Reference Appendix C) Small lymphocytic lymphoma (SLL) or chronic lymphocytic leukemia (CLL)\r\n* Patients will be eligible in >= first complete remission (CR1) with molecularly negative disease\r\n* Patients in CR with molecularly positive disease or in PR will be excluded from autologous transplant Pathologic diagnosis per local institutional review of Richter syndrome that transformed from chronic lymphocytic leukemia (CLL). Chronic lymphocytic leukemia/small lymphocytic lymphoma (SLL) Diagnosis of Chronic Lymphocytic Leukemia (CLL) established according to International Workshop Chronic Lymphocytic Leukemia (IWCLL) criteria. Known transformation of Chronic Lymphocytic Leukemia (CLL) to an aggressive B-cell malignancy at the time of screening Cohort 4: Participants must have chronic lymphocytic leukemia. Known immunosuppressive disease, for example HIV infection or history of bone marrow transplant or chronic lymphocytic leukemia (CLL) Treatment naïve or previously treated Chronic Lymphocytic Leukemia (CLL) requiring treatment Subject who has high-risk chronic lymphocytic leukemia/small lymphocytic lymphoma. Confirmed diagnosis of Chronic Lymphocytic Leukemia (CLL) Patients must have histologically identified chronic lymphocytic leukemia (CLL) or small lymphocytic lymphoma (SLL) as defined by the World Health Organization (WHO) classification of hematopoietic neoplasms Patients must have an indication for treatment by 2008 International Workshop on Chronic Lymphocytic Leukemia (IWCLL) criteria Participants must have confirmed CLL/small lymphocytic lymphoma (SLL) relapsed after at least one prior therapy and currently in need of treatment by IWCLL 2008 criteria Clinically significant and ongoing immune suppression including, but not limited to, systemic immunosuppressive agents such as cyclosporine or corticosteroids, chronic lymphocytic leukemia (CLL), uncontrolled human immunodeficiency virus (HIV) infection, or solid organ transplantation Small lymphocytic lymphoma (SLL) with absolute lymphocyte count < 5 x 10*9/L at the time of diagnosis and at study entry. Chronic lymphocytic leukemia (CLL). Histologically confirmed B-cell non-Hodgkin lymphoma (B-NHL), Chronic Lymphocytic Leukemia (CLL)/Small Lymphocytic Lymphoma (SLL) Previously treated Chronic Lymphocytic Leukemia (CLL) requiring treatment Confirmed diagnosis of mantle cell lymphoma (MCL), chronic lymphocytic leukemia (CLL), or small lymphocytic lymphoma (SLL) CLL/SLL patients must have:\r\n* Indication for treatment according to the 2008 International Workshop on Chronic Lymphocytic Leukemia (IWCLL) criteria\r\n* Received at least one prior standard treatment regimen Documented previously untreated CLL according to the International Workshop on Chronic Lymphocytic Leukemia (IWCLL) criteria Subject must have a diagnosis of CLL that meets 2008 Modified International Workshop on Chronic Lymphocytic Leukemia National Cancer Institute-Working Group (iwCLL NCI-WG) criteria Diagnosis of CLL per diagnostic criteria for relapsed or refractory CLL per the international workshop on chronic lymphocytic leukemia (iwCLL) guidelines Documented CD19+ chronic lymphocytic leukemia (CLL) or small lymphocytic lymphoma (SLL) Diagnosis of relapsing/refractory or previously untreated chronic lymphocytic leukemia Small lymphocytic lymphoma (SLL) with absolute lymphocyte count < 5 x 109/L at the time of diagnosis and at study entry Histologically confirmed diagnosis of follicular lymphoma grade 3b or transformed disease and chronic lymphocytic leukemia (CLL) Diagnosis of chronic lymphocytic leukemia (CLL) or small lymphocytic lymphoma (SLL) that meets protocol-defined criteria Active disease meeting at least 1 of the International Workshop on Chronic Lymphocytic Leukemia 2008 criteria for requiring treatment Prior treatment for chronic lymphocytic leukemia. Histologically-confirmed advanced solid tumor, chronic lymphocytic leukemia, small lymphocytic lymphoma, T-cell prolymphocytic leukemia, Non-Hodgkin Lymphoma or multiple myeloma Diagnosis of chronic lymphocytic leukemia (CLL)/small lymphocytic leukemia (SLL), previously untreated, Rai stage 0-ll Ages =< 50 years of age with chronic lymphocytic leukemia (CLL) Chronic lymphocytic leukemia that has failed induction therapy or Rai stages 2-4 Must have a documented diagnosis of B-cell CLL (IWCLL guidelines for the diagnosis and treatment of chronic lymphocytic leukemia [Hallek, 2008]). Patients will have a diagnosis of chronic lymphocytic leukemia (CLL), small lymphocytic lymphoma (SLL), or cluster of differentiation (CD)20 positive low-grade lymphoproliferative disorder Small lymphocytic lymphoma (SLL), or chronic lymphocytic leukemia (CLL) with progressive disease following standard therapy; or Relapsed or refractory Chronic Lymphocytic Leukemia and require treatment in opinion of investigator Patients with lymphoma (non-Hodgkin lymphoma [NHL], chronic lymphocytic leukemia/small lymphocytic lymphoma [CLL/SLL] or Hodgkin's lymphoma) with primary refractory or relapsed disease after standard chemotherapy at high risk of relapse with conventional autografting; patients with a diagnosis of CLL (or small lymphocytic lymphoma) or diagnosis of CLL that progresses to prolymphocytic leukemia (PLL), or T-cell CLL or PLL Diagnosis of B-cell CLL, established according to International Workshop on Chronic Lymphocytic Leukemia (IWCLL) criteria and having received at least 2 prior treatment regimens Diagnosis of B-cell CLL, with diagnosis established according to International Workshop on Chronic Lymphocytic Leukemia (IWCLL) Small lymphocytic lymphoma (SLL) with absolute lymphocyte count < 5 x 10^9/L at the time of diagnosis Histologically confirmed Richter's transformation (RT) from chronic lymphocytic leukemia/small lymphocytic lymphoma (CLL/SLL). Diagnosis of Chronic lymphocytic leukemia or Small lymphocytic lymphoma that meets at least one of the International Workshop on Chronic Lymphocytic Leukemia (IWCLL) 2008 criteria for treatment (Binet Stage ? B and/or Rai Stage ? I with symptoms) History of chronic leukemias (eg, chronic lymphocytic leukemia). Documented diagnosis of B-cell CLL, according to International Workshop on Chronic Lymphocytic Leukemia 2008 Clinically significant and ongoing immune suppression including, but not limited to, systemic immunosuppressive agents such as cyclosporine or corticosteroids, chronic lymphocytic leukemia (CLL), uncontrolled human immunodeficiency virus (HIV) infection, or solid organ transplantation T cell large granular lymphocytic leukemia Small lymphocytic lymphoma (SLL) with absolute lymphocyte count Patients with CD20-expressing B-cell NHL that is relapsed or refractory to standard therapy. Chronic Lymphocytic Leukemia/Small Lymphocytic Lymphoma with peripheral blood leukemia/lymphoma cells and high-grade lymphomas are excluded Patients must have histologically confirmed Chronic Lymphocytic Leukemia Small Lymphocytic Lymphoma. Chronic lymphocytic leukemia (CLL) Low-grade non-Hodgkin’s lymphoma or plasma cell neoplasm with either of the following, and with stable disease or better prior to transplantation:\r\n* Progressed during multiagent therapy, failed at least two prior therapies (excluding single agent rituximab), or there is evidence of prior transformation\r\n* Small lymphocytic lymphoma (SLL) or chronic lymphocytic leukemia (CLL) with 11q or 17p deletion or with progression < 6 months after a purine analog-containing regimen At least two prior treatment regimens for chronic lymphocytic leukaemia. CLL, Grade 3b follicular lymphoma or evidence that the indolent lymphoma has transformed to aggressive lymphoma. Subjects suspicious for transformation should undergo a biopsy to exclude the possibility of transformation. Subjects with a previous diagnosis of small lymphocytic leukemia (SLL) and a screening monoclonal B-lymphocyte count of ? 5000/µl are defined by 2008 International Workshop on Chronic Lymphocytic Leukemia (IWCLL) criteria to have CLL; such patients are NOT eligible for this study. Small lymphocytic lymphoma (SLL) Patients with chemo-sensitive chronic lymphocytic leukemia (CLL) with persistent or recurrent disease after fludarabine-based regimens, no evidence of \bulky\ disease (> 10 cm in diameter) Previously untreated Chronic Lymphocytic Leukemia (CLL) requiring treatment according to the National Cancer Institute (NCI) criteria Chronic lymphocytic leukemia, small lymphocytic lymphoma (SLL), or grade 3 follicular lymphoma PHASE I: Histological confirmation of relapsed (recurrent after previous therapy[ies]) or refractory (no response to previous therapy[ies]) B-cell NHL; note: patients with small lymphocytic lymphoma (SLL) are eligible however patients with chronic lymphocytic leukemia (CLL) are not eligible Small lymphocytic lymphoma (SLL) or chronic lymphocytic leukemia (CLL) with 17p deletion, or with progression < 6 months after second or greater treatment regimen; must have the following to be an acceptable candidate as well:\r\n* =< 20% of bone marrow cellularity involved by SLL/CLL (to lower risk of graft rejection)\r\n* No lymph nodes >= 5 cm in any dimension\r\n* No massive splenomegaly, defined as > 6 cm below the left costal margin Patients with lymphoproliferative disorders such as chronic lymphocytic leukemia and indolent non-Hodgkin’s lymphoma who are in remission or asymptomatic after initial treatment and are being followed with active surveillance will be eligible. Prior exposure to ABT-199 or B-cell chronic lymphocytic leukemia (CLL)/lymphoma 2 (BCL2) inhibitors Chronic lymphocytic leukemia (CLL) patients with IgG less than 500 mg/dl with/without symptoms who are either untreated or previously treated, regardless of response, at least 6 months from prior therapy (including monoclonal antibody [mAb]) Newly diagnosed aggressive lymphoma or CLL/small lymphocytic lymphoma (SLL) that meets disease specific criteria below: Chronic lymphocytic leukemia (CLL). Active cancer or metastatic disease, except in the case of stage 0 chronic lymphocytic leukemia or nonmelanoma skin cancer No concurrent, active malignancy, other than non-metastatic skin cancer of any type, superficial bladder cancer, or early stage chronic lymphocytic leukemia (well-differentiated small cell lymphocytic lymphoma) or < stage IV follicular lymphoma; if a prior malignancy is in remission for >= 3 years then the patient is eligible Must have a confirmed diagnosis of chronic lymphocytic leukemia or small lymphocytic lymphoma as per International Workshop on Chronic Lymphocytic Leukemia (IW-CLL) 2008 criteria with biopsy proven transformation to diffuse large B cell lymphoma (DLBCL), consistent with Richter’s Syndrome Food and Drug Administration (FDA)-approved indications for idelalisib of relapsed, histologically confirmed B-cell indolent non-Hodgkin lymphoma (iNHL) or chronic lymphocytic leukemia (CLL) Patient has a diagnosis of chronic lymphocytic leukemia Confirmed diagnosis of Chronic Lymphocytic Leukemia (CLL)