Patients must have fewer than 20% marrow blasts within 60 days of consent. Cytogenetic analysis must be performed from diagnostic bone marrow (preferred) or if adequate number of circulating blasts from peripheral blood; FISH testing for common B-lineage ALL abnormalities including t(9;22) (BCR/ABL1), t(12;21) (ETS-variant gene 6 [ETV6]/runt-related transcription factor 1 [RUNX1]), t(1;19) (pre-B-cell leukemia homeobox 1 [PBX1]/transcription factor 3 [TCF3]), +4,+10,+17, (centromeric [Cen]4/Cen10/Cen17), t(11q23;var), (myeloid/lymphoid or mixed lineage leukemia [MLL]), deletion (del)(9p) (cyclin-dependent kinase inhibitor 2A [CDKN2A]/Cen9), and t(14;var) (immunoglobulin heavy chain [IGH] is encouraged); if there are few or no circulating blasts and an adequate marrow sample cannot be obtained for cytogenetic analysis, the patient may still enroll on the trial Patient has one of the following: \r\n* Patients has previously untreated de novo AML and meets the criteria for AML with >= 20% bone marrow blasts as set out in the World Health Organization (WHO) Myeloid Neoplasm classification\r\n** Attempts to obtain bone marrow either by aspirate or biopsy must be made unless clinically prohibitive; in cases where it is clinically prohibitive, peripheral blood with an excess of 20% blasts and in which adequate flow cytometric and cytogenetics/FISH testing is feasible can be substituted for the marrow exam at diagnosis\r\n* Patients has cytopenias and/or bone marrow blasts but does not meet the criteria for the diagnosis of AML (WHO Myeloid Neoplasm classification) because of < 20% marrow blasts and meets the criteria for a diagnosis of myelodysplastic syndrome (MDS)\r\n* Patients has a history of transient myeloproliferative disorder (which may or may not have required chemotherapy intervention), who:\r\n* Are > 8 weeks since resolution of transient myeloproliferative disease (TMD) with >= 5% blasts, OR\r\n* Patients who have an increasing blast count (>= 5%) in serial bone marrow aspirates performed at least 4 weeks apart In the event that the patient’s bone marrow blast count is >= 50% blasts, patients may be registered but should receive steroids for 3-5 days in order to reduce tumor burden prior to blinatumomab administration, as follows\r\n* Prephase treatment with dexamethasone (10-20 mg/m^2) for 3-5 days is required for patients with bone marrow blasts >= 50%, peripheral blood blasts 15,000/uL or higher, or elevated lactate dehydrogenase (LDH) suggesting rapidly progressive disease per investigator opinion\r\n** Pre-treatment should conclude at least 24 hours prior to the first dose of blinatumomab (although additional dexamethasone is automatically given as a pre-med prior to the first dose); at the time of first infusion of blinatumomab, the absolute peripheral blast count should be < 25,000/uL\r\n** Note: For the purposes of the study, day 1 of the cycle will be the first day of blinatumomab administration Patients with MDS must have experienced treatment failure with at least one cycle of hypomethylating therapy or induction therapy and have ? 10% bone marrow blasts Patients must have evidence of acute leukemia in their peripheral blood or bone marrow; patients must have >= 5% blasts in the peripheral blood or bone marrow within 14 days prior to registration; at least >= 20% of those blasts must be CD22-positive (surface) based on local immunophenotyping and histopathology Acute myeloid leukemia (AML), myelodysplastic syndrome (MDS)-refractory anemia with excess blasts (RAEB) (including chronic myelomonocytic leukemia [CMML] with excess blasts and MDS/myeloproliferative neoplasm [MPN] overlap syndrome) not in remission (defined as >= 5% blast in bone marrow or peripheral blood) prior to leukemia cell harvest; patients may receive additional cytoreductive therapy after leukemia cell harvest and before admission for transplant, , at the discretion of the treating physician; for patients with MDS-EB1 (< 10%blasts) or CMML-1, it is recommended that they proceed directly to transplant after the harvest if donor is available; if there is an extended delay, interval therapy with HMA is allowed\r\n* Patients may or may not have active disease at the time of transplant conditioning, but for reduced intensity conditioning (RIC) candidates, it is strongly recommended that disease is cytoreduced such that the pre-transplant admission marrow shows:\r\n** < 30% blasts in a normocellular marrow (>= 50% cellularity), or\r\n** < 50% blasts in a hypocellular marrow (< 50% cellularity) Myelodysplasia (MDS)/myeloproliferative syndrome (MPS): patients must have < 5% marrow blasts at time of transplant Presence of circulating leukemic blasts (in the peripheral blood) detected by standard pathology for patients with AML, ALL or CML Presence of >= 5% circulating leukemic blasts (in the peripheral blood) detected by standard pathology for patients with MDS/MPS Hyperleukocytosis with ? 30,000 leukemic blasts/µL blood (hydroxyurea permitted up to 24 hours prior to beginning study drugs) MDS - Marrow blasts must be > 5% and disease failed at least 1 prior hypomethylating agent More than 5% blasts in bone marrow Patients must have IPSS score determined by cytogenetic analysis prior to randomization; patients with cytogenetic failure and =< 10% marrow blasts will be eligible Participant with lymphoma must meet one of the following:\r\n* In first relapse, OR\r\n* Refractory to one or two courses of frontline induction therapy with measurable disease\r\n* Relapse in ALL is defined as the reappearance (in a patient who has previously achieved remission) of leukemic blasts in the bone marrow or peripheral blood\r\n** Should flow cytometric analyses suggest relapse (by the reappearance of a similar immunophenotype to the original leukemia) in the presence of < 5% blasts morphologically, a repeat bone marrow test is recommended to confirm relapse\r\n** Molecular or genetic relapse is characterized by the reappearance of a cytogenetic or molecular abnormality\r\n** Early relapse is defined as relapse on therapy or < 6 months after completion of frontline therapy; late relapse is defined as relapse occurring >= 6 months after completion of frontline therapy Fewer than 20% blasts in the bone marrow or peripheral blood Had accelerated phase or leukemic transformation (>= 10% blasts in peripheral blood [PB] or bone marrow [BM] any time prior to HCT) Peripheral blood blasts ? 10% Prior chemotherapy for AML. Hydroxyurea is allowed for the control of peripheral leukemic blasts in subjects with leukocytosis Morphological disease in the bone marrow (? 5% blasts) Bone marrow blasts of at least 10% Patient must be diagnosed with acute leukemia in morphologic complete remission (CR1 or CR2) or with MDS with no circulating blasts and with less than 5% blasts in the bone marrow Patients who are currently undergoing or who previously underwent allogeneic HCT for \r\n* Acute myeloid leukemia (AML) of any subtype and any of the following:\r\n** With relapse or refractory disease (>= 5% marrow blasts by morphology, or circulating blasts, chloroma or granulocytic sarcoma) at the time of the pre-HCT work-up\r\n** With minimal/measurable residual disease (MRD: defined as detectable disease by morphology, flow cytometry, molecular or cytogenetic testing but < 5% marrow blasts by morphology, no circulating blasts) at the time of the pre-HCT work-up\r\n** With marrow aplasia or marked hypoplasia (bone marrow cellularity =< 10%) following chemotherapy for prior refractory AML at the time of the pre-HCT work-up\r\n** With relapse or refractory disease (>= 5% marrow blasts by morphology, or circulating blasts) at any time after HCT\r\n** With MRD at any time after HCT\r\n* Acute lymphoid leukemia (ALL) of any subtype and any of the following:\r\n** With relapse or refractory disease (>= 5% marrow blasts, or circulating blasts) at the time of the pre-HCT work-up\r\n** With MRD at the time of the pre-HCT work-up\r\n** With marrow aplasia or marked hypoplasia (bone marrow cellularity =< 10%) following chemotherapy for prior refractory ALL at the time of the pre-HCT work-up\r\n** With relapse or refractory disease (>= 5% marrow blasts, or circulating blasts) at any time after HCT\r\n** With MRD at any time after HCT\r\n* Biphenotypic/undifferentiated/any other type of acute leukemia and any of the following:\r\n** With relapse or refractory disease (defined as detectable disease by morphology, flow cytometry, molecular or cytogenetic testing but < 5% marrow blasts by morphology, no circulating blasts) at the time of the pre-HCT work-up\r\n** With MRD at the time of the pre-HCT work-up\r\n** With marrow aplasia or marked hypoplasia (bone marrow cellularity =< 10%) following chemotherapy for prior refractory acute leukemia at the time of the pre-HCT work-up\r\n** With relapse or refractory disease (>= 5% marrow blasts, or circulating blasts) at any time after HCT\r\n** With MRD at any time after HCT \r\n* Chronic myeloid leukemia with a history of blast crisis and \r\n** With relapse or refractory disease (>= 5% marrow blasts, or circulating blasts) at any time after HCT\r\n** With persistent rising minimal residual disease (defined as detectable disease by morphology, flow cytometry, molecular or cytogenetic testing but < 5% marrow blasts by morphology, no circulating blasts on >= 2 of two consecutive tests), refractory or ineligible for treatment with tyrosine kinase inhibitors at any time after HCT Confirmation of ‘measurable disease’ by blast % will be defined as a marrow blast percentage of > 5% by morphologic assessment on bone marrow examination; this criteria does not apply to myeloid sarcoma which must also show measurable lesion by computed tomography (CT), magnetic resonance imaging (MRI), positron emission tomography (PET)/CT or photograph (i.e. Leukemia cutis); if marrow blasts of =< 5% blasts are enumerated the patient may be eligible only if there is clear (probable or definite) flow cytometric, cytogenetic or molecular aberrations (e.g. FLT3-ITD, NPM1, etc.) documenting relapse of the leukemia associated clone defined prior to HCT Presence of circulating blasts (in the blood) detected by standard pathology for patients with AML, ALL or CML Presence of >= 5% circulating leukemic blasts (in the blood) detected by standard pathology for patients with MDS/MPS/CMML Must have a diagnosis of chronic phase (CP) (defined as peripheral blood and bone marrow < 10% blasts) primary myelofibrosis (PMF) or post essential thrombocythemia (post-ET) or polycythemia vera (post-PV) myelofibrosis by World Health Organization (WHO) criteria OR a diagnosis of a myeloproliferative neoplasm in accelerated/blast phase (MPN-AP/BP) defined as either a peripheral blood or bone marrow with >= 10% blasts Use of hydroxyurea is permitted to control blasts until day -3 AML ONLY: AML with > 30% circulating blasts and > 50% bone marrow blasts Acute leukemias: Must be in remission by morphology (< 5% blasts); NOTE: cytogenetic relapse or persistent disease without morphologic relapse is acceptable; also a small percentage of blasts that is equivocal between marrow regeneration versus (vs.) early relapse are acceptable provided there are no associated cytogenetic markers consistent with relapse No blasts or promyelocytes in peripheral blood Patients with AML must have less than 10% bone marrow blasts and < 100/mcL absolute peripheral blood blast count For subjects with ALL or AML, presence of >5% blasts in the bone marrow (based on a bone marrow aspirate/biopsy sample with ?200 nucleated cells and the presence of bone marrow spicules) and/or >1 x 109/L blasts in the peripheral blood (with the restriction that peripheral blast count in subjects with AML must be <50 x 109/L prior to the start of study therapy). Blasts in Peripheral Blood or Bone Marrow ?15% (either myeloid or lymphoid blasts) Promyelocytes and Blasts in Peripheral Blood or Bone Marrow ?30% Cytogenetic clonal evolution Blast phase is defined as ?30% blasts in peripheral blood or bone marrow, or presence of extramedullary disease, except for liver or spleen. Relapsed ALL defined as > 5% malignant blasts in bone marrow or peripheral blood Diagnosis of relapsed or refractory AML, ALL, acute biphenotypic leukemia (assigned to the appropriate group by the treating physician and pathology/cytogenetics), advanced MDS defined as ?10% bone marrow blasts, advanced MPN, MDS/MPN overlap syndrome with ?10% bone marrow blasts, or advanced CML after failure of at least 3 TKIs Diagnosis of relapsed or refractory AML, ALL, acute biphenotypic leukemia (assigned to the appropriate group by the treating physician and pathology/cytogenetics), advanced MDS defined as ?10% bone marrow blasts, advanced MPN, MDS/MPN overlap syndrome with ?10% bone marrow blasts, or advanced CML after failure of at least 3 TKIs Acute leukemias: Must be in remission by morphology (< 5% blasts); Note cytogenetic relapse or persistent disease without morphologic relapse is acceptable; also a small percentage of blasts that is equivocal between marrow regeneration vs. early relapse are acceptable provided there are no associated cytogenetic markers consistent with relapse Very high risk pediatric patients with AML: Patients < 21 years, however, are eligible with (M2 marrow) with < 25% blasts in marrow after having failed one or more cycles of chemotherapy Subjects must have evaluable disease defined as > 5% blasts on marrow aspirate or biopsy, extramedullary disease (central nervous system [CNS] involvement is prohibited), or at least 20% blasts in the peripheral blood within 4 weeks prior to enrollment; Note: subjects with second or subsequent relapse are considered to have evaluable disease even without having > 5% marrow blasts if they are found to have persistent/recurrent disease-associated molecular or cytogenetic abnormalities at any time since their last cycle of intensive chemotherapy Expectation that we can obtain about 10 million blasts from blood and/or marrow (e.g., circulating blast count of 5,000 or greater or cellular marrow with greater than or equal to 20% blasts) Disease criteria: day 21 (+/-7 days) bone marrow aspiration or biopsy from the beginning of salvage DCIA: a. in complete morphologic remission with < 5% bone marrow blasts, or b. aplastic (< 10% bone marrow cellularity), and cytopenic with an absolute neutrophil count (ANC) less than 1,000/uL, or c. low disease burden with < 30% bone marrow (BM) blasts, with recovery of peripheral blood (PB) white blood cell (WBC) (ANC > 1,000/uL) and < 5% circulating blasts For cohort 1 only: patients with a bone marrow biopsy with < 15% cellularity, evidence of collagen fibrosis, osteosclerosis, or blasts > 10% in peripheral blood or marrow (demonstrating advanced disease) RECIPIENT: Patients may have evidence of MDS with one or more peripheral blood cytopenias and greater than 5% blasts but less than 10% blasts in the bone marrow in the absence of filgrastim Acute myeloid leukemia who fail to achieve complete remission with one course of induction chemotherapy or after relapse; patients must have less than 20% bone marrow or peripheral blood blasts Patients with CML-AP or CML-BP or Philadelphia chromosome-positive acute myeloid leukemia defined as follows: CML-AP is defined by the presence of 15-29% blasts in peripheral blood (PB) or bone marrow (BM), >= 20% basophils in PB or BM, >= 30% blasts plus promyelocytes (with blasts < 30%) in PB or BM, < 100 x 10^9/L platelets unrelated to therapy, or by clonal cytogenetics evolution (i.e., the presence of cytogenetic abnormalities other than the Philadelphia chromosome); CML-BP is defined by the presence of >= 30% blasts in the bone marrow and/or peripheral blood or the presence of extramedullary disease Aspartate aminotransferase (AST) =< 5 x the institutional ULN, measured prior to conditioning chemotherapy; elevation secondary to leukemic involvement is not an exclusion criterion; leukemic involvement will be determined by the presence of progressive relapse defined by escalating bone marrow or peripheral blood leukemia blasts within the previous month and the absence of initiation of known hepatotoxic medication (e.g. azoles) Presence of less than 20% bone marrow blasts per bone marrow Acute leukemias (includes T lymphoblastic lymphoma); remission is defined as < 5% blasts with no morphological characteristics of acute leukemia (e.g., Auer rods) in a bone marrow with > 20% cellularity, peripheral blood counts showing ANC > 1000/ul, including patients in complete remission with incomplete platelet recovery (CRp); if the marrow has < 20% cellularity due to treatment related cytotoxicity, but still has < 5% blasts, an exception may be made to include this patient up to principal investigator (PI) discretion Myeloproliferative disorder (MPD)\r\n* Life-threatening cytopenia(s), and/or red blood cell or platelet transfusion dependence\r\n* Patients with aplasia\r\n* Patients with excess blast less than or equal to 10% blasts in the bone marrow at work-up Myelodysplastic syndrome (MDS): Any subtype; morphologic blasts must be less than 5% in an evaluable marrow (> 25% of normal cellularity for age); if blasts are 5% or more, patient requires induction chemotherapy pre-transplant to reduce blast count to less than 5%; patients who have a hypocellular marrow in the absence of excess blasts that is related to the underlying disease or as a result of treatment for MDS may also be eligible with the approval of the PI or designee Greater than 30% blasts in bone marrow or greater than 5% in peripheral blood Very high risk pediatric patients with AML; patients < 21 years, however, are eligible with (M2 marrow) with < 25% blasts in marrow after having failed one or more cycles of chemotherapy; this group of patients will be analyzed separately Acute leukemias: must be in remission by morphology (< 5% blasts); note cytogenetic relapse or persistent disease without morphologic relapse is acceptable; also a small percentage of blasts that is equivocal between marrow regeneration vs. early relapse are acceptable provided there are no associated cytogenetic markers consistent with relapse Unless in post-chemotherapy and radioimmunoconjugated antibody induced aplasia, when he/she would be eligible, patients with acute leukemia in morphologic relapse/persistent disease defined as > 5% blasts in normocellular bone marrow OR any % blasts if blasts have unique morphologic markers (e.g. Auer rods) or associated cytogenetic markers that allows morphologic relapse to be distinguished are not eligible Acute leukemias: must be in remission by morphology (=< 5% blasts); also a small percentage of blasts that is equivocal between marrow regeneration versus (vs.) early relapse are acceptable provided there are no associated cytogenetic markers consistent with relapse Very high risk pediatric patients with AML: patients < 21 years, however, are eligible with (M2 marrow) with < 25% blasts in marrow after having failed one or more cycles of chemotherapy <5% blasts in marrow or blood at time of screening <1% peripheral blood blasts. <10% bone marrow blasts. Acute myeloid leukemia-intermediate risk as defined by standard World Health Organization (WHO) criteria for AML (at least 20% blasts in the peripheral blood or bone marrow) at the time of initial diagnosis\r\n* Diagnosis of AML according to WHO diagnostic criteria (at least 20% blasts in the peripheral blood or bone marrow), with French–American–British (FAB) classification other than M3 (acute promyelocytic leukemia), documented by bone marrow aspiration and biopsy performed within 14 days prior to administration of 1st dose of remission induction chemotherapy More than 5% blasts in bone marrow Presence of >= 5% abnormal blasts in the bone marrow Have previously untreated AML, defined according to WHO criteria, with ? 20% leukemic blasts in the bone marrow. Subjects with extramedullary disease alone (ie, no detectable bone marrow and no detectable peripheral blood AML) are not eligible for the study. Bone marrow blasts >5% at randomization, OR Subjects who have been diagnosed as having AML with peripheral blood or bone marrow blasts of ?20%. Cytogenetic analysis must be performed from diagnostic bone marrow (preferred) or if adequate number of circulating blasts (> 10^9/l) from peripheral blood Circulating blasts < 20,000 (cytoreduction with hydroxyurea is allowed) Acute lymphocytic leukemia- high risk CR1 as evidenced by high risk cytogenetics [eg t(9;22) or complex cytogenetic abnormalities] or > 1 cycle to obtain CR; second or greater CR; must be in remission by morphology; patients in morphologic relapse/persistent disease defined as > 5% blasts in normocellular bone marrow OR any % blasts if blasts have unique morphologic markers or associated cytogenetic markers that allows morphologic relapse to be distinguished are not eligible for arms 2 or 3; note cytogenetic relapse or persistent disease without morphologic relapse is acceptable; also a small percentage of blasts that is equivocal between marrow regeneration vs early relapse is acceptable provided there are no associated cytogenetic markers consistent with relapse Patients must have > 5% blasts in the bone marrow at the time of study enrollment Blasts in the peripheral blood (PB) and bone marrow (BM) < 20% prior to study enrollment Accelerated phase myeloproliferative neoplasm (MPN) as defined by 10%-19% blasts in the peripheral blood or bone marrow and evidence of dysplastic marrow features with a concomitant diagnosis of essential thrombocythemia (ET), polycythemia vera (PV) or primary myelofibrosis (PMF) or a diagnosis of acute myelogenous leukemia as defined by 20% blasts in the blood or bone marrow following a previous diagnosis of ET, PV or PMF Leukemic transformation (> 10% blasts in peripheral blood or bone marrow biopsy). Relapsed or refractory AML patients with at least 5% blasts by bone marrow biopsy or aspirate, or at least 1% blasts in peripheral blood, not likely to benefit from standard salvage chemotherapy. MDS: Patients must have < 10% marrow blasts; fewer than 10% marrow blasts must be documented by marrow examination within 3 weeks of initiation of conditioning CMML: Patients with CMML1 who have not received myelosuppressive therapy must have < 10% marrow blasts; fewer than 10% marrow blasts must be documented by marrow examination within 3 weeks of initiation of conditioning; OR patients with CMML who have progressed beyond CMML1 and have received myelosuppressive chemotherapy must have < 5% marrow blasts; fewer than 5% marrow blasts must be documented by marrow examination within 3 weeks of initiation of conditioning MPD: Patients must have < 10% marrow blasts; fewer than 10% marrow blasts must be documented by marrow examination within 3 weeks of initiation of conditioning Atypical CML: Patients must have < 10% marrow blasts; fewer than 10% marrow blasts must be documented by marrow examination within 3 weeks of initiation of conditioning Presence of >= 5% circulating leukemic blasts (in the peripheral blood) detected by standard pathology Aspartate aminotransferase (AST) =< 5 x the institutional ULN; elevation secondary to leukemic involvement is not an exclusion criterion; leukemic involvement will be determined by the presence of progressive relapsed defined by escalating bone marrow or peripheral blood leukemia blasts within the previous month and the absence of initiation of known hepatotoxic medication (e.g. azoles) Presence of circulating leukemic blasts in the peripheral blood detected by standard morphology CMML with 10% to 19% myeloblasts in the bone marrow and/or 5% to 19% blasts in the blood. OR Worl health organisation (WHO) Classifications: RAEB 2 - defined as having 10% to 19% myeloblasts in the bone marrow and/or 5% to 19% blasts in the blood. CMML 2 - defined as having 10% to 19% myeloblasts in the bone marrow and/or 5% to 19% blasts in the blood. CMML 1 (Although CMML 1 is defined as having <10% myeloblasts in the bone marrow and/or <5% blasts in the blood, these participants may enroll only if bone marrow blasts >=5%. Active AML (bone marrow blasts >= 5% by morphology, staining, or flow) and/or presence of extramedullary disease Patients with previously untreated primary AML who meet the customary criteria for AML with >= 20% bone marrow blasts as set out in the 2008 World Health Organization (WHO) Myeloid Neoplasm Classification are eligible\r\n* Attempts to obtain bone marrow either by aspirate or biopsy must be made unless clinically prohibitive; in cases where it is clinically prohibitive, peripheral blood with an excess of 20% blasts and in which adequate flow cytometric and cytogenetics/fluorescent in situ hybridization (FISH) testing is feasible can be substituted for the marrow exam at diagnosis Patients must have measureable disease as defined the presence of >= 5% blasts in bone marrow or extramedullary leukemia Participants must have a diagnosis of AML or MDS and must have disease that has relapsed or is refractory to chemotherapy, or that has relapsed after hematopoietic stem cell transplantation (HSCT)\r\n* Refractory disease is defined as persistent disease after at least two courses of induction chemotherapy\r\n* Patients with AML must have>= 5% leukemic blasts in the bone marrow or increasing levels of minimal residual disease (MRD) in the bone marrow as assessed by flow cytometry; if an adequate bone marrow sample cannot be obtained, patients may be enrolled if there is unequivocal evidence of leukemia in the peripheral blood Morphological disease in the bone marrow (? 5% blasts) Blast phase disease (> 20% blasts in the marrow or peripheral blood) Documented excessive leukemic myeloid blasts in the bone marrow or peripheral blood (>= 10%) in the past 6 months All patients must meet one of the qualifications as outlined below after prior HMA therapy:\r\n* Relapse after CR/CRi or partial remission (PR) - 1 or more of the following:\r\n** Return to pretreatment bone marrow blast percentage (for initial PR)\r\n** Reappearance of bone marrow blasts (> 5%) following initial CR/CRi\r\n* Disease progression\r\n** For patients with 10% to 20% blasts: a 50% or more increase to more than 20% blasts\r\n** For patients with > 20% blasts: a 50% or more increase to more than 40% blasts\r\n* Refractory disease\r\n** No evidence of a response (CR, CRi, PR) following, at least, 6 cycles of hypomethylating agent Subjects must have a diagnosis of relapsed or refractory ALL with ? 5% blasts in the bone marrow (M2 or M3 disease), with or without extramedullary disease. -To be eligible, subjects must have had 1 or more prior therapeutic attempts, defined as: Disease refractory or relapsed (defined as the reappearance of > 5% blasts in the bone marrow). Pathological diagnosis of AML according to WHO criteria (with at least 20% blasts in the peripheral blood or bone marrow) Any acute leukemia (including prior myelodysplasia or CML blast crisis) with morphologic relapse or persistent disease >= 10% blasts in the bone marrow (BM), or doubling of the blasts in the blood in the 2 weeks preceding admission, or need for hydroxyurea in the 2 weeks prior to admission, or uncontrolled extra-medullary disease <5% blasts in blood or marrow at screening Patients with advanced MDS must have < 10% marrow blasts prior to receiving conditioning with TLI/ATG; less than 10% marrow blasts must be documented by marrow examination within 1 month of starting conditioning; if necessary, a cytoreductive regimen will be determined by referring centers Patients with MPD must have < 10% marrow blasts prior to receiving conditioning with TLI/ATG; less than 10% marrow blasts must be documented by marrow examination within 1 month of starting conditioning; if necessary, a cytoreductive regimen will be determined by referring centers Patients with evolution to AML are required to be in a morphologic leukemia-free state with blasts less than 5% in a marrow aspirate; presence of residual dysplastic features following cytoreductive therapy is acceptable Therapy-related myeloid neoplasms:\r\n* Patients with therapy related-MDS (t-MDS) must have < 10% marrow blasts prior to receiving conditioning with TLI/ATG; less than 10% marrow blasts must be documented by marrow examination within 1 month of starting conditioning; if necessary, a cytoreductive regimen will be determined by referring centers Presence of circulating leukemic blasts (in the peripheral blood) detected by standard pathology for patients with AML, ALL or CML Presence of >= 5% circulating leukemic blasts (in the peripheral blood) detected by standard pathology for patients with MDS/MPS Blasts in Peripheral Blood or Bone Marrow ?15% Promyelocytes and Blasts in Peripheral Blood or Bone Marrow ?30% Thrombocytopenia <100 x 103/ml, not resulting from therapy Blast phase is defined as ?30% blasts in peripheral blood or bone marrow, or presence of extramedullary disease, except for liver or spleen. 20% blasts in bone marrow Patients must have obtained a complete remission with chemotherapy defined by the absence of circulating blasts, and less than 5% blasts on bone marrow examination following hematopoietic recovery Patients must have >= 5% blasts by morphology in the bone marrow OR molecular evidence of at least 0.1% leukemic blasts in the bone marrow Morphological evidence of disease in bone marrow (at least 5% blasts) Relapse in ALL is defined as the reappearance (in a patient who has previously achieved remission) of leukemic blasts in the bone marrow\r\n* Should flow cytometric analyses suggest relapse (by the reappearance of a similar immunophenotype to the original leukemia) in the presence of < 5% blasts morphologically, a repeat bone marrow test is recommended to confirm relapse\r\n* Molecular or genetic relapse is characterized by the reappearance of a cytogenetic or molecular abnormality Patients with T-cell ALL must have greater than 25% blasts in the bone marrow with or without extramedullary disease. Patients must have received at least one prior chemotherapy regimen for their AML and they may have received any type of chemotherapy; disease relapse or the presence of refractory disease must be documented by bone marrow examination demonstrating > 5% blasts in the bone marrow not attributable to another cause; administration of hydrea to control high white blood cell (WBC) count is permitted Bone marrow aspirate/biopsy results showing >5% blasts Remission will be defined as < 5% blasts in the peripheral blood and bone marrow without morphological characteristics of the original leukemia population at the time of diagnosis Patients with AML in the first morphologic relapse as defined by >= 5% reappearance of leukemia blasts in the bone marrow not attributable to any other cause who have not yet received chemotherapy for the current relapse Participants must have a diagnosis of AML or MDS and must have disease that has relapsed or is refractory to chemotherapy, or that has relapsed after hematopoietic stem cell transplantation (HSCT)\r\n* Refractory disease is defined as persistent disease after at least two courses of induction chemotherapy\r\n* Patients with AML must have >= 5% leukemic blasts in the bone marrow or have converted from negative minimal residual disease (MRD) status to positive MRD status in the bone marrow as assessed by flow cytometry; if an adequate bone marrow sample cannot be obtained, patients may be enrolled if there is unequivocal evidence of leukemia in the peripheral blood Non-M3 acute myeloid leukemia (AML) with the presence of residual disease in the bone marrow on day 14-28 post induction (or re-induction) chemotherapy; day 14-28 residual disease is defined in this study as the presence of more than 10 % blasts in the marrow in patients, presence of between 5-10% blasts cells that are not in cluster in hypocellular marrow is ambiguous and bone marrow biopsy should be repeated in 5-7 days < 5% blasts in blood or marrow at screening, except if measurable extramedullary AML is confirmed Leukemic transformation (> 20% blasts in PB or bone marrow [BM] any time prior to hematopoietic cell transplantation [HCT]) Patients must have > 10% leukemic blasts in the bone marrow; Greater than 5% blasts in bone marrow Patients must have a strong clinical suspicion of JMML, based on a modified category 1 of the revised diagnostic criteria; specifically, eligible patients must have all of the following: \r\n* Splenomegaly\r\n* Absolute monocyte count (AMC) > 1000/uL\r\n* Blasts in peripheral blood (PB)/bone marrow (BM) < 20% Relapsed or refractory (resistant) disease, as defined by standard criteria:\r\n* Relapsed: bone marrow blasts >= 5%; reappearance of blasts in the blood; development of extramedullary disease\r\n* Refractory (resistant): failure to achieve CR or CRi in patients who survive >= 7 days following completion of initial treatment, with evidence of persistent leukemia by blood and/or bone marrow examination Blast phase disease (>20% blasts in the marrow or peripheral blood) Patients with AML must have less than 30% bone marrow blasts and no peripheral blood blasts Transformed disease (bone marrow blasts are permitted; however, transformed disease indicating leukemic involvement is not permitted) Leukemic relapse or disease progression: Patients with > 25% leukemic blasts in the bone marrow will not be eligible for DLI; cytoreduction with chemotherapy is permissible to reduce blast count to =< 25% Patients must have >= 5% blasts in the bone marrow Patients must have had histologic verification of AML at original diagnosis; AML is defined according to World Health Organization (WHO) classification with >= 5% blasts in the bone marrow (M2/M3 bone marrow), with or without extramedullary disease Diagnosis of acute lymphoblastic leukemia (ALL) or acute myeloid leukemia (AML) with < 5% blasts in the bone marrow (M1) by morphology and that meets one of the following criteria:\r\n* Flow cytometric evidence of minimal residual disease (MRD) (>= 0.1% leukemic blasts for ALL or < 5% leukemic blasts for AML detected in the bone marrow) OR\r\n* Molecular/cytogenetic evidence of disease (fluorescence in situ hybridization [FISH] or polymerase chain reaction [PCR] methodology) performed within 7 days AND\r\n* With the intent of going on to an allogeneic hematopoietic cell transplantation (allo-HCT) independent of this study Patients must have documented hypoplasia from the bone marrow aspiration and biopsy 14 days +/- 2 days from the initiation of cytarabine treatment schedule (defined as < 5% blasts and < 20% cellularity) Acute Leukemias: Must be in remission by morphology (< 5% blasts); Note cytogenetic relapse or persistent disease without morphologic relapse is acceptable; also a small percentage of blasts that is equivocal between marrow regeneration versus early relapse are acceptable provided there are no associated cytogenetic markers consistent with relapse Patients with acute leukemia in morphologic complete remission with or without hematologic recovery or with myelodysplasia (MDS) with no circulating blasts and with less than 5% blasts in the bone marrow. Patients with CMML must have a WBC count ? 10,000 cells/µL and < 5% blasts in the marrow. Patients with ? 5% blasts due to a regenerating marrow must contact the protocol chairs for review. Subjects with acute leukemia, chronic myelogenous leukemia, or myelodysplasia must have no circulating blasts and < 5% blasts of the bone marrow. Less than or equal to 5% blasts on bone marrow examination within 60 days of starting conditioning EXCLUSION CRITERIA FOR ENROLLMENT (PRE-TRANSPLANT): Active leukemia (> 5% leukemic blasts in peripheral blood or bone marrow) EXCLUSION CRITERIA (PRIOR TO IBRUTINIB ADMINISTRATION): Relapsed leukemia (> 5% leukemic blasts in peripheral blood or bone marrow after allogeneic HCT) Patients with acute leukemia or chronic myelogenous leukemia with no circulating blasts and with less than 10% blasts in the bone marrow MDS\r\n* Bone marrow with =< 5 percent myeloblasts with normal maturation of all cell lines\r\n* Peripheral blood demonstrates hemoglobin >= 11 g/dL, platelets >= 100 x 10^9/L, neutrophils >= 1 x 10^9/L, and no circulating blasts Myelodysplasia (MDS)/myeloproliferative syndrome (MPS) – Patients must have < 5% marrow blasts at time of transplant Acute leukemias: Must be in remission by morphology (=< 5% blasts); also a small percentage of blasts that is equivocal between marrow regeneration versus early relapse are acceptable provided there are no associated cytogenetic markers consistent with relapse Pre-injectable HMA (HYPOMETHYLATING AGENT) baseline bone marrow myeloblasts: a. Less than 5%: ? 100% increase to ? 8% blasts b. ? 5%: ? 50% increase to ? 10% blasts Note: ? 30% blasts is considered AML (ACUTE MYELOID LEUKEMIAT) per FAB (FRENCH-AMERICAN BRITISH)classification. Subjects known to have ? 30% blasts are not eligible for inclusion in this study. RECOG (Eastern Cooperative Oncology Group) nizing limitations of blast cell quantification, this protocol will allow subjects with pre-enrollment bone marrow blast counts up to 33% on the screening bone marrow examination to be considered for inclusion. Assessment may be made according to local bone marrow examination to facilitate enrollment of eligible subjects into the treatment phase of the study. Patients with acute leukemia, chronic myelogenous leukemia, myeloproliferative disorder and myelodysplasia with no circulating blasts and with less than 5% blasts in the bone marrow within 4 weeks of the start of transplant conditioning regimen Patients with acute leukemia, chronic myelogenous leukemia or myelodysplasia with no circulating blasts and with less than 5% blasts in the bone marrow. Patients must have obtained a complete remission with chemotherapy defined by the absence of circulating blasts, and less than 5% blasts on bone marrow examination following hematopoietic recovery The patient has a confirmed diagnosis of Philadelphia chromosome (Ph) positive chronic myelogenous leukemia in either CP or AP. Accelerated phase will be defined as disease having 1 of the following: ?15% to <30% blasts in peripheral blood or bone marrow; ?30% blasts + promyelocytes in peripheral blood or bone marrow; ?20% basophils in peripheral blood or bone marrow; platelet count <100x109/L unrelated to therapy; or clonal evolution.