Acute myeloid leukemia (AML) is an aggressive form of cancer characterized by the abnormal proliferation of hematopoietic progenitor cells that disrupts normal cell differentiation, leading to serious health complications. Although AML is a rare malignancy, its poor prognosis and low overall survival rates represents a serious health challenge. Among the drivers implicated in the development and progression of AML, is the FMS-like tyrosine kinase 3 (FLT3) enzyme, which is frequently mutated in AML and is associated with poor outcomes. FLT3 mutations result in constitutive activation of the FLT3 receptor, leading to dysregulated cellular proliferation and survival. To combat this, several kinase inhibitors targeting FLT3 have been developed, with the aim of inhibiting the aberrant signalling pathway and improving patient outcomes. Among these kinase inhibitors, three agents have gained approval from the US FDA for the treatment of AML. Additionally, there are candidate inhibitors currently approved or under review by the FDA for indications other than AML but have potent activity against FLT3 and are being evaluated in clinical trials for various AML indications at present. This review focuses on the significance of FLT3 mutations in AML and the FDA-approved or under review kinase inhibitors targeting FLT3 with emphasis on their profile, limitations, and current clinical status regarding AML therapy.