Simple Summary: Despite intensive standard treatment, acute myeloid leukemia (AML) continues to be associated with a poor prognosis due to treatment resistance and a high risk of relapse. For this reason, it is necessary to develop new therapeutic strategies, which, when used in combination with standard treatment, can increase the chances of patient survival. One of them might be the use of CAR-T cells. In the following review, we present the latest reports on the use of anti-CD33, -CD123, -FLT3 or -CLL-1 CAR-T cells in (pre-)clinical trials, as well as the emerging challenges of the proposed therapy. The use of CAR-T cells in common clinical practice in the treatment of AML will only be possible after further research, the focus of which should be the myeloablative effect of CAR-T cells, the eradication of cells in the immunosuppressive environment of the tumor, and their life span in the body. In order to increase the effectiveness of cancer therapies and extend the long-term survival of patients, more and more often, in addition to standard treatment, oncological patients receive also targeted therapy, i.e., CAR-T cells. These cells express a chimeric receptor (CAR) that specifically binds an antigen present on tumor cells, resulting in tumor cell lysis. The use of CAR-T cells in the therapy of relapsed and refractory B-type acute lymphoblastic leukemia (ALL) resulted in complete remission in many patients, which prompted researchers to conduct tests on the use of CAR-T cells in the treatment of other hematological malignancies, including acute myeloid leukemia (AML). AML is associated with a poorer prognosis compared to ALL due to a higher risk of relapse caused by the development of resistance to standard treatment. The 5-year relative survival rate in AML patients was estimated at 31.7%. The objective of the following review is to present the mechanism of action of CAR-T cells, and discuss the latest findings on the results of anti-CD33, -CD123, -FLT3 and -CLL-1 CAR-T cell therapy, the emerging challenges as well as the prospects for the future. [ABSTRACT FROM AUTHOR]