The advent of chimeric antigen receptor (CAR) engineering has led to the development of powerful cellular therapies for cancer. CAR T cell-based treatments have had notable clinical success, but logistical issues and associated toxicities are recognized limitations. There is emerging interest in using other immune effector cell types for CAR therapy. Natural killer (NK) cells are part of the innate immune system, and these lymphocytes play major roles in immunosurveillance and antitumor immune responses. Incorporating CARs into NK cells provides the opportunity to harness and enhance their innate cytotoxic potential toward malignancies. In this review, we discuss the production of CAR-engineered NK cells, highlight data on their preclinical and clinical efficacy, and examine the obstacles and strategies to overcome them.