• PRE-REGISTRATION ELIGIBILITY CRITERIA

• Newly diagnosed acute myeloid leukemia (AML) associated with antecedent myeloproliferative disorder (polycythemia vera, essential thrombocythemia, myelofibrosis, atypical chronic myeloid leukemia, chronic myelomonocytic leukemia and related undifferentiated myeloproliferative/myelodysplastic disorders)

• Relapsed/refractory AML associated with antecedent myeloproliferative disorder (polycythemia vera, essential thrombocythemia, myelofibrosis, atypical chronic myeloid leukemia, chronic myelomonocytic leukemia and related undifferentiated myeloproliferative/myelodysplastic disorders) who have received two or fewer prior induction chemotherapy courses

• Accelerated phase myeloproliferative disorders per Zeider et al with two or fewer prior therapies

‣ For aggressive phase myeloproliferative disorders (MPD) (polycythemia vera, essential thrombocythemia, Philadelphia \[Ph\]-negative chronic myelogenous leukemia), one or more of the following criteria must be met: marrow blasts \> 5%, peripheral blood blasts plus progranulocytes \> 10%, new onset or increasing myelofibrosis, new onset or \> 25% increase in hepatomegaly or splenomegaly, new onset constitutional symptoms (fever, weight loss, splenic pain, bone pain). Zeider et al

⁃ For chronic myelomonocytic leukemia (CMML), the following criteria must be met: 5-19% bone marrow blasts (aggressive) or \>= 20% marrow blasts (transformation)

• Bone marrow and/or peripheral blood specimens will be submitted for correlative studies; patients with a dry tap will still be eligible

• RANDOMIZATION ELIGIBILITY CRITERIA

• Bone marrow aspirate and/or peripheral blood specimens were submitted to the central lab and site has confirmation by the local institution that the patient meets one of the criteria specified above

• Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 or Karnofsky \>= 60%

• Total bilirubin less than 2.0 mg/dL unless due to Gilbert's syndrome, then less than 5.0 mg/dL

• Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) less than 5 x institutional upper limit of normal

• Creatinine clearance glomerular filtration rate (GFR) greater than 30 ml/min per modified Cockcroft-Gault formula

• Interval of greater than 4 weeks since allogeneic blood or marrow transplantation (BMT) if performed; and absence of active graft versus host disease (GVHD)

• The effects of veliparib on the developing human fetus are unknown; for this reason and because PARP inhibiting agents as well as topoisomerase inhibitors and platinating agents are known to be teratogenic, women of child-bearing potential must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry, for the duration of study participation, and for 6 months following the last dose of study drug; should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately; men treated or enrolled on this protocol must also agree to use adequate contraception prior to the study, for the duration of study participation, and 4 months after completion of veliparib administration

• Ability to understand and the willingness to sign a written informed consent document