The field of cell therapy is leading a paradigm shift in drug development. The recent convergence of several fields, including immunology, genetics, and synthetic biology, now allows for the introduction of artificial receptors and the design of entire genetic circuitries to finely program the behavior of injected cells. A prime example of these next-generation living drugs comes in the form of T cells expressing chimeric antigen receptors (CARs), which have already demonstrated definitive evidence of therapeutic efficacy against some hematological malignancies. However, several obstacles still restrict the antitumor efficacy of and impair the widespread use of CAR-T cells. Critical challenges include limited persistence and antitumor activity in vivo, antigen escape, scarcity of suitable single markers for targeting, and therapy-related toxicity. Nevertheless, intense research activity in this field has resulted in a plethora of creative solutions to address each of these limitations. In this review, we provide a comprehensive snapshot of the current strategies used to enhance the therapeutic efficacy, applicability, and safety of genetically engineered immune cells to treat cancer.