Inclusion Criteria:

1. Must be at least 18 years of age.
2. Patients must have relapsed/refractory leukemias for which no standard therapies exist. Patients with poor-risk myelodysplasia (MDS) and chronic myelomonocytic leukemia (CMML) who failed prior therapy are also candidates for this protocol. Relapsed/refractory leukemias include acute non-lymphocytic leukemia (AML) by WHO classification (i.e. >/= 20% blasts), acute lymphocytic leukemia (ALL), or chronic myelogenous leukemia (CML) in blast crisis. Patients with CML who are resistant to at least two tyrosine kinase inhibitors and have no standard stem cell transplant option are also eligible.
3. ECOG performance status of 0-2.
4. A female of childbearing potential must have a negative serum or urine pregnancy test at screening. Women of child-bearing potential must use acceptable contraceptive methods, and must have a negative serum or urine pregnancy test within 2 weeks prior to beginning treatment on this trial. Nursing patients are excluded. Sexually active men must also use acceptable contraceptive methods for the duration of time on study.
5. Must be able and willing to give written informed consent.
6. In the absence of rapidly progressing disease, the interval from prior treatment to time of study drug administration should be at least 2 weeks for cytotoxic agents, or at least one week for noncytotoxic agents. Persistent clinically significant toxicities from prior chemotherapy must not be greater than grade 2.
7. Patients must have the following clinical laboratory values unless considered due to leukemic organ involvement: 1.) Serum creatinine less than or equal to 2.0 mg/dl. 2.) Total bilirubin less than or equal to 1.5x the upper limit of normal unless considered due to Gilbert's syndrome or hemolysis. 3.) Alanine aminotransferase (ALT), and aspartate aminotransferase (AST) less than or equal to 2.5x the upper limit of normal unless considered due to organ leukemic involvement (then 5x).
8. Patients with active CNS disease are included and will be treated concurrently with intrathecal therapy. INCB018424 will not be administered by intrathecal route.

Exclusion Criteria:

1. Uncontrolled intercurrent illness including, but not limited to uncontrolled infection, symptomatic congestive heart failure, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements.
2. Active heart disease including myocardial infarction within the previous 3 months, symptomatic coronary artery disease, arrhythmias not controlled by medication, or uncontrolled congestive heart failure.
3. Current treatment or treatment within 2 weeks or 5 half-lives (whichever is longer) prior to the first dose of study medication with another investigational medication or current enrollment in another investigational drug protocol (unless there is evidence of rapidly progressive disease in which case a shorter interval from last therapy may be acceptable).
4. Females who are pregnant or are currently breastfeeding.
5. Patients receiving therapy with intermediate or high dose steroids greater than the equivalent of 10 mg prednisone per day are not allowed.
6. Evidence of active hepatitis or human immunodeficiency virus (HIV) infection determined by screening laboratory test results or results within prior 3 months.
7. Any unresolved toxicity equal to or greater than Grade 2 from previous anticancer therapy, except for stable chronic toxicities not expected to resolve, such as peripheral neurotoxicity.
8. Incomplete recovery from any prior surgical procedures or had surgery within 4 weeks prior to study entry, excluding the placement of vascular access.
9. Uncontrolled intercurrent illness or any concurrent condition that, in the Investigator's opinion, would jeopardize the safety of the patient or compliance with the protocol.
10. In patients who are receiving medications known to be inhibitors or inducers of CYP3A4 every effort will be made to change these medications to acceptable alternatives. If this is not safely possible, patients will be excluded from participation in the study. If a patient is already on the study, must be started on a CYP3A4 inhibitor, and is demonstrating benefit from the study, they will be seen twice weekly in the first cycle and weekly in the subsequent cycles for toxicity evaluation and their dose will be modified in the event of a toxicity related to the study drug.