Despite several small-molecule drugs that have revolutionized the current treatment strategy for acute myeloid leukemia (AML), hematopoietic stem cell transplantation remains the only curative treatment in most cases to date. Chimeric antigen receptor (CAR)-T cell therapy is one of the most promising next-generation cancer therapies for hematological malignancies and is clinically available for treatment of AML. However, developing AML-targeted CAR-T therapy is challenging because of the heterogeneity of target antigen expression across leukemic cells and patients, the difficulty in excluding on-/off-target tumor effects, and the immunosuppressive tumor microenvironment. To date, various targets, including CD33, NKG2D, CD123, CLL-1, and CD7, have been actively studied for CAR-T cells. Although no CAR-T cell products are close to practical use, several clinical trials have shown promising results, particularly for CAR-T cells targeting CLL-1 or CD123. Meanwhile, research exploring the ideal target for AML-targeted CAR-T therapy continues. Furthermore, as collecting autologous lymphocytes from patients with AML is difficult, development of off-the-shelf CAR-T products is being actively pursued. This review discusses the challenges in AML-targeted CAR-T cell therapy development from the perspectives of target antigen characteristics and AML-specific on-target/off-tumor toxicity. Moreover, it discusses the clinical development and prospects of AML-targeting CAR-T cells.