Inclusion Criteria:

          -  Diagnosis requirement for phase I patients:

               -  Refractory AML without complete remission (CR) after induction therapy (primary
                  induction failure) or relapsed AML after obtaining a CR.

               -  OR High-risk AML (by ELN criteria; See Appendix C) in complete remission (CR) and
                  has either refused hematopoietic stem cell transplantation OR is currently not
                  eligible for hematopoietic stem cell transplantation OR for whom hematopoietic
                  stem cell transplantation is being reserved for later relapse. This is inclusive
                  of patients with minimal residual disease evidenced by cytogenetics, molecular
                  testing, and/or flow cytometry.

               -  OR Myelodysplastic syndrome (MDS) with excess blasts (>5%) and progressive
                  disease at any time after initiation of DNA hypomethylator treatment during the
                  past 2 years, OR failure to achieve complete or partial response or hematological
                  improvement (see section 12.4) after at least six cycles of azacytidine or four
                  cycles of decitabine administered during the past 2 years, OR intolerance to
                  azacytidine or decitabine. MDS patients with isolated 5q- abnormalities that meet
                  these criteria after lenalidomide therapy and DNA hypomethylator therapy are also
                  eligible.

          -  Diagnosis requirement for phase II patients:

             *Refractory AML without CR after induction therapy (primary induction failure) or
             relapsed AML after obtaining a CR. Favorable-risk core binding factor (CBF) mutated
             AML and acute promyelocytic leukemia (APL) will be excluded.

          -  Diagnosis requirement for pediatric cohort patients:

             *Refractory AML without complete remission (CR) after induction therapy (primary
             induction failure) or relapsed AML after obtaining a CR.

          -  Age requirement for phase I and phase II patients: At least 18 years of age.

          -  Age requirement for pediatric cohort: 2-17 years of age.

          -  Available HLA-haploidentical donor that meets the following criteria:

               -  Related donor (parent, sibling, offspring, or offspring of sibling)

               -  At least 18 years of age

               -  HLA-haploidentical donor/recipient match by at least Class I serologic typing at
                  the A&B locus.

               -  In general good health, and medically able to tolerate leukapheresis required for
                  harvesting the NK cells for this study.

               -  Negative for hepatitis, HTLV, and HIV on donor viral screen

               -  Not pregnant

               -  Voluntary written consent to participate in this study

          -  Patients with known CNS involvement with AML are eligible provided that they have been
             treated and CSF is clear for at least 2 weeks prior to enrollment into the study. CNS
             therapy (chemotherapy or radiation) should continue as medically indicated during the
             study treatment.

          -  Karnofsky/Lansky performance status ≥ 50 %

          -  Adequate organ function as defined below:

               -  Total bilirubin ≤ 2 mg/dL

               -  AST(SGOT)/ALT(SGPT) ≤ 3.0 x IULN

               -  Creatinine within normal institutional limits OR creatinine clearance ≥ 50
                  mL/min/1.73 m2 by Cockcroft-Gault Formula (adults) or Schwartz formula (pediatric
                  cohort)

               -  Oxygen saturation ≥90% on room air

               -  Ejection fraction ≥35%

          -  Able to be off corticosteroids and any other immune suppressive medications beginning
             on Day -3 and continuing until 30 days after the infusion of the CIML NK cells.
             However, use of low-level corticosteroids is permitted if deemed medically necessary.
             Low-level corticosteroid use is defined as 10mg or less of prednisone (or equivalent
             for other steroids) per day.

          -  Women of childbearing potential must have a negative pregnancy test within 28 days
             prior to study registration. Female and male patients (along with their female
             partners) must agree to use two forms of acceptable contraception, including one
             barrier method, during participation in the study and throughout the DLT evaluation
             period.

          -  Ability to understand and willingness to sign an IRB approved written informed consent
             document (or that of legally authorized representative, if applicable).

        Exclusion Criteria:

          -  Relapsed after allogeneic transplantation.

          -  Isolated extramedullary relapse (phase II only).

          -  More than one course of salvage chemotherapy for primary induction failure or AML
             relapsing after CR1 (phase II only).

          -  Circulating blast count ≥30,000/µL by morphology or flow cytometry (cytoreductive
             therapies including leukapheresis or hydroxyurea are allowed).

          -  Uncontrolled bacterial or viral infections, or known HIV, Hepatitis B or C infection.

          -  Uncontrolled angina, severe uncontrolled ventricular arrhythmias, or EKG suggestive of
             acute ischemia or active conduction system abnormalities.

          -  New progressive pulmonary infiltrates on screening chest x-ray or chest CT scan that
             have not been evaluated with bronchoscopy. Infiltrates attributed to infection must be
             stable/ improving after 1 week of appropriate therapy (4 weeks for presumed or proven
             fungal infections).

          -  Known hypersensitivity to one or more of the study agents.

          -  Received any investigational drugs within the 14 days prior to the first dose of
             fludarabine.

          -  Pregnant and/or breastfeeding.