The FLT3 receptor is overexpressed on the majority of acute myeloid leukemia (AML) blasts. Mutations in FLT3 are the most common genetic alteration in AML, identified in approximately one third of newly diagnosed patients. FLT3 internal tandem duplication mutations (FLT3-ITD) are associated with increased relapse and inferior overall survival. Multiple small molecule inhibitors of FLT3 signaling have been identified, two of which (midostaurin and gilteritinib) are currently approved in the United States, and many more of which are in clinical trials. Despite significant advances, resistance to FLT3 inhibitors through secondary FLT3 mutations, upregulation of parallel pathways, and extracellular signaling remains an ongoing challenge. Novel therapeutic strategies to overcome resistance, including combining FLT3 inhibitors with other antileukemic agents, development of new FLT3 inhibitors, and FLT3-directed immunotherapy are in active clinical development. Multiple questions regarding FLT3-mutated AML remain. In this review, we highlight several of the current most intriguing controversies in the field including the role of FLT3 inhibitors in maintenance therapy, the role of hematopoietic cell transplantation in FLT3-mutated AML, use of FLT3 inhibitors in FLT3 wild-type disease, significance of non-canonical FLT3 mutations, and finally, emerging concerns regarding clonal evolution.