The goal of this clinical research study is to find the highest tolerable dose of nivolumab that can be give in combination with idarubicin and cytarabine in patients with MDS and AML. The safety and effectiveness of this drug combination will also be studied.

This is an investigational study. Nivolumab is not FDA-approved or commercially available. Idarubicin is FDA-approved and commercially available for the treatment of patients with AML. Cytarabine is FDA approved and commercially available for treatment of patient with AML. The use of these drugs in combination is investigational. The study doctor can explain how the drugs are designed to work.

Up to 75 patients will take part in this study. All will be enrolled at MD Anderson.

Study Groups:

If you are found to be eligible to take part in this study, you will be assigned to a study group based on when you join this study. Up to 3 groups of 3 - 6 participants will be enrolled in Phase 1 of the study, and up to 70 participants will be enrolled in Phase 2.

If you are enrolled in Phase 1, the dose of nivolumab you receive will depend on when you join this study. There are 3 dose levels being tests in this part of the study: a low dose, a middle dose, and a high dose. The first group of participants will receive the middle dose level of nivolumab. If no intolerable side effects are seen, the next group will receive the highest dose level. However, if there are intolerable side effects, 3 more participants will receive the middle dose. If there are further intolerable side effects seen, the next group will receive the lowest dose of nivolumab.

If you are enrolled in Phase 2, you will receive nivolumab at the highest dose that was tolerated in Phase 1.

All participants will receive the same dose levels of idarubicin and cytarabine.

Study Drug Administration:

You will receive 1- 7 cycles of the drug combination. These cycles will be 28-35 days long.

• On Days 1-3 of each cycle, you will receive idarubicin by vein over about 15-30 minutes.
• On Days 1-4 of each cycle, you will receive cytarabine by vein over about 24 hours. If you are age 60 or older, you will receive the drugs on Days 1-3 only. On these days you will receive drugs to help decrease the risk of side effects.
• On Day 24 (+/- 2 days) of each cycle, you will receive nivolumab by vein over about 1 hour.

After 2 cycles, if the disease appears to get better, you will receive nivolumab by vein about every 2 weeks for up to 1 year.

Study Visits:

At least one (1) time a week during Cycle 1 and then at least once each cycle after that:

• You will have a physical exam.
• Blood (about 2-3 teaspoons) will be drawn for routine tests.

You will have a bone marrow aspirate collected for cytogenetics testing between Day 21-28 of each cycle and then, if the doctor thinks it is needed, you will have this performed every 1-2 weeks after that unless a complete response is achieved. After that, you will have bone marrow collected every 3-6 months for 1 year.

After your last dose of study drug, you will have a physical exam.

Length of Study:

You may continue taking nivolumab for up to 1 year. You will no longer be able to take the study drug if the disease gets worse, if intolerable side effects occur, or if you are unable to follow study directions.

Your participation on the study will be over after the follow-up visits.

Inclusion Criteria:

1. Diagnosis of 1) AML (WHO classification definition of >/= 20% blasts), or 2) high risk MDS (defined as the presence of 10% blasts).
2. Patients aged 18 to 60 years are eligible. Patients older than 60 who are deemed fit to receive intensive chemotherapy by the treating physician are eligible after discussion with the PI.
3. In the Phase I portion, patients with relapsed or refractory AML/MDS are also eligible, as per the treating physician's discretion.
4. For the Phase II portion of the study, patients must be chemo-naive, i.e. not have received any prior chemotherapy (except hydrea or one dose of ara-C </= 2g) for AML or MDS. They could have received hypomethylator agents, transfusions, hematopoietic growth factors or vitamins. Temporary prior measures such as apheresis or hydrea or one dose of ara-C </= 2g in order to safely control hyperleucocytosis prior to enrollment.
5. Serum biochemical values with the following limits unless considered due to leukemia: ---Creatinine </= 1.5 mg/dl --- total bilirubin </= 1.5 mg/dL, unless increase is due to hemolysis or congenital disorder --- transaminases (SG PT) </= 2.5 x upper limit of normal (ULN).
6. Ability to take oral medication.
7. Ability to understand and provide signed informed consent.
8. Baseline test of ejection fraction must be >/= 50%.
9. Performance status < 3, unless directly related to disease process as determined by the Principal Investigator.

Exclusion Criteria:

1. Subjects with APL.
2. Any coexisting medical condition that in the judgment of the treating physician is likely to interfere with study procedures or results.
3. Nursing women, women of childbearing potential with positive urine pregnancy test, or women of childbearing potential who are not willing to maintain adequate contraception (such as birth control pills, IUD, diaphragm, abstinence, or condoms by their partner) over the entire course of the study. --- Women of childbearing potential (WOCBP) must use appropriate method(s) of contraception. WOCBP should use an adequate method to avoid pregnancy for 23 weeks (30 days plus the time required for nivolumab to undergo five half-lives) after the last dose of investigational drug. --- Women of childbearing potential must have a negative serum or urine pregnancy test (minimum sensitivity 25 IU/L or equivalent units of HCG) within 24 hours prior to the start of nivolumab. --- Women must not be breastfeeding.
4. Continued:Men who are sexually active with WOCBP must use acceptable birth control methods. Acceptable birth control methods include: oral or injectable hormonal birth control, intrauterine devices(IUDS), and double barrier methods (for example a condom in combination with spermicide). Men receiving nivolumab and who are sexually active with WOCBP will be instructed to adhere to contraception for a period of 31 weeks after the last dose of investigational product Women who are not of childbearing potential (ie, who are postmenopausal or surgically sterile as well as azoospermic men do not require contraception.
5. Cardiac disease: Congestive heart failure > class II NYHA. Patients must not have unstable angina (anginal symptoms at rest) or new onset angina (began within the last 3 months) or myocardial infarction within the past 6 months.
6. History of cardiac ventricular arrhythmias requiring anti-arrhythmic therapy within past 3 months.
7. Thrombotic or embolic events such as a cerebrovascular accident including transient ischemic attacks within the past 6 months.
8. Pulmonary hemorrhage/bleeding event > CTCAE Grade 2 within 4 weeks of first dose of study drug.
9. Major surgery, open biopsy or significant traumatic injury within 4 weeks of first study drug.
10. Active clinically serious and uncontrolled infection > CTCAE Grade 2 uncontrolled with antibiotics.
11. Patients should be excluded if they have an active, known or suspected autoimmune disease. Subjects are permitted to enroll if they have vitiligo, type I diabetes mellitus, residual hypothyroidism due to autoimmune condition only requiring hormone replacement, psoriasis not requiring systemic treatment, or conditions not expected to recur in the absence of an external trigger.
12. Patients should be excluded if they are known to be positive test for hepatitis B virus surface antigen (HBV sAg) or hepatitis C virus ribonucleic acid (HCV antibody) indicating acute or chronic infection.
13. Patients should be excluded if they have known history of testing positive for human immunodeficiency virus (HIV) or known acquired immunodeficiency syndrome (AIDS).
14. History of allergy to study drug components.
15. Prior immune checkpoint targeting drugs (e.g., anti PD1, and PDL1, anti-kir, anti CD137...etc)