Current objectives regarding treatment for acute myeloid leukemia (AML) include achieving complete remission (CR) by clinicopathological criteria followed by interrogation for the presence of minimal/measurable residual disease (MRD) by molecular genetic and/or flow cytometric techniques. While advances in molecular genetic technologies have enabled highly sensitive detection of AML-associated mutations and translocations, determination of MRD is complicated by the fact that many treated patients have persistent clonal hematopoiesis that may not reflect residual AML. Clonal hematopoiesis detected in AML patients in CR includes true residual or early recurrent AML, myelodysplastic syndrome (MDS) or clonal hematopoiesis that is ancestral to the AML, and independent or newly emerging clones of uncertain leukemogenic potential. While the presence of AML-related mutations has been shown to be a harbinger of relapse in multiple studies, the significance of other types of clonal hematopoiesis is less well understood. In patients who undergo allogeneic hematopoietic cell transplantation (HCT), post-HCT clones can be donor-derived and in some cases engender a new myeloid neoplasm that is clonally unrelated to the recipient's original AML. In this article, we discuss the spectrum of clonal hematopoiesis that can be detected in treated AML patients, propose terminology to standardize nomenclature in this setting, and review clinical data and areas of uncertainty among the various type of post-treatment hematopoietic clones.