Decitabine and Talazoparib in Untreated AML and R/R AML

The purpose of this study is to find the best way to combine a new chemotherapy drug with one that is already in use to treat AML. The new experimental drug is called talazoparib (also known as BMN-673), and it is not approved by the Federal Drug Administration (FDA). The FDA is allowing the use of talazoparib for the purposes of this study. Decitabine is used to treat bone marrow diseases called myelodysplastic syndromes (MDS), as well as off label for AML. Lab work suggests that talazoparib will increase the effects of decitabine in leukemia cells. Investigators hope that treating patients with decitabine and talazoparib together will be more successful that treating patients with decitabine alone. This study has two parts. The purpose of part one the study is to find out the best doses of decitabine and talazoparib to use when they are given together to treat AML. The purpose of part two is to see how well the drugs work together to treat AML. All participants in the study will be treated with decitabine and talazoparib. Part one of the study will include as few as two people and as many as 36 people to find the best dose levels of the study drugs. Part one will begin enrolling first. Part two of the study will not start until the Part one of the study is complete. Participants will be told which part of the study they may be enrolled in. Part two of the study may include as few as 79 people and as many as 135 people. Part two includes three separate arms. Participants enrolled in Part two of the study, will be assigned to one of the three arms below in order to test the success rate of the study drug dose determined by Part one: * Arm A will enroll adult patients with AML who are thought not to be likely to tolerate or respond to standard chemotherapy; * Arm B will enroll adult patients with AML that has not responded to previous treatment or has come back after responding to previous treatment; * Arm C will enroll adult patients previously treated with a DNA methyltransferase inhibitor (decitabine, azacitidine or guadecitabine). This is a multi-center study. Up to 171 people may take part in this study globally.