Inclusion Criteria:

- Patients must express human leukocyte antigen (HLA)-A*0201

- Patients undergoing matched allogeneic hematopoietic cell transplantation (HCT) for:

- A) Acute Myeloid Leukemia (AML) including:

- AML beyond first remission, therapy-related AML at any stage, primary refractory
AML, AML in relapse (before or after HCT), AML with evidence of minimal residual
disease (MRD) at time of HCT or after HCT (by multiparameter flow cytometry,
cytogenetics, fluorescence in situ hybridization [FISH] or molecular studies);
AML at any stage arising in a patient with an antecedent diagnosis of a
hematologic disorder including myelodysplastic or myeloproliferative syndrome
(e.g. chronic myelomonocytic leukemia, polycythemia vera, essential
thrombocytosis, and agnogenic myeloid metaplasia with myelofibrosis)

- AML at any stage with unfavorable cytogenetic or molecular abnormalities:
Monosomal karyotype (presence of two or more distinct autosomal chromosome
monosomies or a single autosomal monosomy associated with at least one
structural abnormality), del(5q)/-5, -7/del(7q), abn 3q, 9q, 11q, 20q, 21q, 17p,
t(6;9), t(9;22), complex karyotype (>= 3 unrelated abnormalities), Inv(3) or
t(3;3), t(6;11), +8 sole,+8 with 1 other abnormality other than t(8;21),
t(9;11), inv (16), t(16;16), t(11;19), or normal cytogenetics with fms-related
tyrosine kinase 3 (FLT3)-internal tandem duplication (ITD) mutation

- B) Myelodysplastic syndrome (MDS) including:

- Intermediate-2 or high risk category patients according to the International
Prognostic Scoring System (IPSS >= 1.5) or poor risk karyotype defined as
abnormalities involving chromosome 7 or complex karyotype (>= 3 unrelated
abnormalities)

- Relapsed disease post HCT

- C) Chronic Myeloid Leukemia (CML) including:

- CML beyond chronic phase

- Relapsed disease post-HCT

- Patients who previously underwent allogeneic HCT for AML, MDS or CML and have
experienced overt relapse or minimal residual disease at any time post-HCT can be
offered enrollment on the protocol and may undergo therapy on Arm 2 of the protocol

- Patients must have an HLA-matched donor of hematopoietic stem cells (related or
unrelated)

- Patients must be able to provide blood and bone marrow samples and undergo the
procedures required for this protocol

- Patients must be >= 50 kg

- Patients must be able to give informed consent; parent or legal representative will
be asked to consent for patients younger than 18 year old

- DONOR: Patient and donor (related or unrelated) must be HLA-matched and express
HLA-A*0201

- DONOR: Donor must be Epstein-Barr virus (EBV) or cytomegalovirus (CMV) seropositive

- DONOR: Donor must be age 18 or older

- DONOR: In good general health

- DONOR: Able to give informed consent

Exclusion Criteria:

- Central nervous system (CNS) tumor refractory to intrathecal chemotherapy and/or
cranio-spinal radiation

- In patients whose leukemic cells are available for evaluation, expression of WT1 will
be determined, and, if leukemic cells are negative for WT1 expression by polymerase
chain reaction (PCR), the patient will be excluded from the study; patients with no
evaluable leukemia will be eligible for enrollment based on the high frequency of
positive leukemias (> 90%), and leukemia will be evaluated for WT1 expression if
recurrence is detected

- Human immunodeficiency virus (HIV) seropositive

- Significant medical or psychological conditions that would make the patient
unsuitable candidate for cell therapy at the discretion of the principal investigator
(PI)

- Pregnancy or breast-feeding; women of childbearing potential must have a negative
serum or urine beta-human chorionic gonadotropin (hCG) pregnancy test result within 7
days before the first dose of WT1-specific T cell infusion; woman of non-childbearing
potential will be defined as being postmenopausal greater than one year or who have
had a bilateral tubal ligation or hysterectomy; all recipients of WT1-specific T
cells will be counseled to use effective birth control during participation in this
study and for 12 months after the last T cell infusion

- DONOR: Less than 18 years old

- DONOR: Active infectious hepatitis

- DONOR: HIV or human T-lymphotropic virus (HTLV) seropositive

- DONOR: Pregnancy or nursing

- DONOR: Significant medical conditions (e.g. immunosuppressive therapy) that would
make the donor unsuitable T cell donor

- DONOR: Unable to give informed consent