The investigators hypothesize that the combination of Pevonedistat/Low-Dose Cytarabine (LDAC) therapy will be tolerable, that a recommended phase 2 dose of Pevonedistat in combination with LDAC will be identified, and that the combination therapy will show evidence of clinical activity in adult patients with Relapsed/Refractory Acute Myelogenous Leukemia (AML) and Advanced Myelodysplastic Syndromes (MDS).

Inclusion Criteria:

A. Confirmed diagnosis of one of the following:

1. Relapsed/refractory Acute Myelogenous Leukemia (AML) where no alternative life prolonging therapy exists. Treatment naïve patients may also be considered eligible if in the opinion of the investigator, these patients are unlikely to benefit from alternative therapy (eg conventional chemotherapy, hypomethylating agents).
2. Relapsed/refractory Myelodysplasic Syndrome (MDS) following at least two courses of a hypomethylating agent (eg azacitidine or decitabine). Patients intolerant of hypomethylating agents (irrespective of the number of cycles administered) will also be considered eligible. MDS eligibility limited to patients with intermediate, high or very high risk based on IPSS-R.

B. Adult male or female patients 18 years of age or older.

C. Eastern Cooperative Oncology Group (ECOG) Performance Status of 0, 1, or 2

D. Patients must satisfy the following laboratory criteria:

1. Albumin > 2.7 g/dL
2. Total bilirubin ≤ upper limit of normal (ULN) except in patients with Gilbert's syndrome. Patients with Gilbert's syndrome may enroll if direct bilirubin ≤1.5 x ULN of the direct bilirubin
3. Alanine transaminase (ALT) and Aspartate transaminase (AST) must be ≤ 2.5 × ULN
4. Creatinine 1.5 x ULN or calculated creatinine clearance > 50ml/min
5. Hemoglobin > 8 g/dL (prior red blood cell (RBC) transfusion allowed). Patients may be transfused to achieve this value. Elevated indirect bilirubin due to post-transfusion hemolysis is allowed.
6. White blood cell (WBC) count < 50,000/µL before administration of PEVONEDISTAT on Cycle 1 Day 1. Note: Hydroxyurea may be used to control the level of circulating leukemic blast cell counts to not lower than 10,000/µL during the study.

E. Suitable venous access to allow for all study related blood sampling (safety and research).

F. Estimated life expectancy, in the judgment of the Investigator, which will permit receipt of at least 6 weeks of treatment.

G. Voluntary written consent must be given before performance of any study related procedure not part of standard medical care, with the understanding that consent may be withdrawn by the patient at any time without prejudice to future medical care.

H. Female patients who:

1. Are postmenopausal (see Appendix for definition) for at least 1 year before the screening visit, OR

2. Are surgically sterile, OR

3. If they are of childbearing potential:

   • Agree to practice 1 highly effective method and 1 additional effective (barrier) method of contraception, at the same time, from the time of signing the informed consent through 4 months after the last dose of study drug (female and male condoms should not be used together), OR
   • Agree to practice true abstinence, when this is in line with the preferred and usual lifestyle of the subject. (Periodic abstinence [eg, calendar, ovulation, symptothermal, postovulation methods] withdrawal, spermicides only, and lactational amenorrhea are not acceptable methods of contraception).

I. Male patients, even if surgically sterilized (ie, status postvasectomy), who:

1. Agree to practice effective barrier contraception during the entire study treatment period and through 4 months after the last dose of study drug (female and male condoms should not be used together), OR
2. Agree to practice true abstinence, when this is in line with the preferred and usual lifestyle of the subject. (Periodic abstinence [eg, calendar, ovulation, symptothermal, postovulation methods for the female partner] withdrawal, spermicides only, and lactational amenorrhea are not acceptable methods of contraception).

J. Able to undergo bone marrow aspiration at screening.

Exclusion Criteria:

A. Treatment with clinically significant metabolic enzyme inducers within 14 days before the first dose of the study drug. Strong CYP3A inhibitors and CYP3A inducers are not permitted during the study.

B. Therapy with any investigational products, anti-neoplastic therapy, or radiotherapy within 14 days prior to Cycle 1 Day 1. Patients actively receiving hydroxyurea are eligible and may continue to receive hydroxyurea during protocol treatment.

C. Candidates for standard and/or potentially curative treatments (a candidate is defined as a patient that is both eligible and willing to have these treatments)

D. Major surgery within 14 days before the first dose of any study drug or a scheduled surgery during study period.

E. Grade 2 or higher diarrhea as defined by NCI CTCAE Version 4.03 despite optimal anti-diarrheal supportive care within 7 days prior to Cycle1 Day1.

F. Known cardiopulmonary disease defined as one of the following:

1. Uncontrolled high blood pressure (ie, systolic blood pressure > 180 mm Hg, diastolic blood pressure > 95 mm Hg).
2. Cardiomyopathy or history of ischemic heart disease; patients with ischemic heart disease who have had acute coronary syndrome (ACS), MI, and/or revascularization greater than 6 months before screening and who are without cardiac symptoms may enroll;
3. Clinically significant arrhythmia including:,history of polymorphic ventricular fibrillation or torsade de pointes); permanent atrial fibrillation [a fib], defined as a fib for ≥6 months; persistent a fib, defined as sustained afib >7 days and/or requiring cardioversion in the 4 weeks before screening; Grade 3 a fib defined as symptomatic and incompletely controlled medically, or controlled with device (e.g., pacemaker), or ablation. Patients with paroxysmal a fib are permitted to enroll. However, patients with < Grade 3 atrial fibrillation (a fib) for a period of at least 6 months may enroll provided that their rate is controlled on a stable regimen.
4. Implantable cardioverter defibrillator;
5. Congestive heart failure (New York Heart Association (NYHA) Class III or IV; or Class II with a recent decompensation requiring hospitalization or referral to a heart failure clinic within 4 weeks before screening), myocardial infarction and/or revascularization (eg, coronary artery bypass graft, stent) within 6 months of first dose of study drug.
6. Moderate to severe aortic and/or mitral stenosis or other valvulopathy (ongoing);
7. Pulmonary hypertension.
8. Patients with Grade 2 or higher prolonged rate corrected QT (QTc) interval (≥ 481msec), calculated according to institutional guidelines.
9. Left ventricular ejection fraction (LVEF) < 50% as assessed by echocardiogram or radionuclide angiography - LVEF assessment is not required for screening, and will only be done at the investigators discretion if clinically indicated..
10. Known moderate to severe chronic obstructive pulmonary disease (COPD), interstitial lung disease, and pulmonary fibrosis.

G. Active uncontrolled infection or severe infectious disease, such as severe pneumonia, meningitis, or septicemia.

H. Known human immunodeficiency virus (HIV) seropositive.

I. Known hepatitis B surface antigen seropositive (Note: Patients who have isolated positive hepatitis B core antibody (ie, in the setting of negative hepatitis B surface antigen and negative hepatitis B surface antibody) must have an undetectable hepatitis B viral load. Patients who have positive hepatitis C antibody may be included if they have an undetectable hepatitis C viral load.)

J. Known or suspected active hepatitis C infections (Patients who are hepatitis C surface antigen-positive are eligible).

K. Females of child bearing potential who refuse to either practice 2 effective methods of contraception at the same time or abstain from heterosexual intercourse from the time of signing the informed consent through 30 days after the last dose of study drug.

L. Males of child bearing potential who refuse to practice effective barrier contraception during the entire study treatment period and through 4 months after the last dose of study drug. (Includes males surgically sterilized - i.e. status post vasectomy).

M. Female patients who are both lactating and breastfeeding or have a positive serum pregnancy test during the screening period or a positive urine pregnancy test on Day 1 before first dose of study drug.

N. Female patients who intend to donate eggs (ova) during the course of this study or 4 months after receiving their last dose of study drug(s).

O. Male patients who intend to donate sperm during the course of this study or 4 months after receiving their last dose of study drug(s).

P. Any serious medical or psychiatric illness that could, in the investigator's opinion, potentially interfere with the completion of study procedures.

Q. Symptomatic central nervous system (CNS) involvement.

R. Diagnosed or treated for another malignancy within 2 years before randomization or previously diagnosed with another malignancy and have any evidence of residual disease. Patients with nonmelanoma skin cancer or carcinoma in situ of any type are not excluded if they have undergone resection.

S. Known hepatic cirrhosis or severe pre-existing hepatic impairment.

T. Systemic anti-neoplastic therapy or radiotherapy within 14 days before the first dose of any study drug, except for hydroxyurea.

U. Patients with uncontrolled coagulopathy or bleeding disorder.

V. Life-threatening illness unrelated to cancer.