TEN-010 is a small molecule, bromodomain and extra-terminal domain (BET) bromodomain inhibitor. This study is designed to characterize the safety, tolerability, and pharmacokinetics of TEN-010 in patients with relapsed/refractory acute myeloid leukemia (RR-AML) and hypomethylating agent (HMA)-refractory myelodysplastic syndrome (MDS). In addition, this trial will assess response to treatment using International Working Group (IWG) response criteria. This study will be conducted in two parts: dose escalation and dose expansion. For dose escalation (Part A), a standard "3+3" design will be used in which successive cohorts of three or more patients with RR-AML or HMA-refractory MDS will be treated at escalating doses until a maximum tolerated dose (MTD) is identified. For the dose expansion part of the study (Part B), patients will be treated with TEN-010 at the MTD (or the highest dose tested if the MTD is not defined) to further characterize its safety, pharmacokinetics, and clinical response.