The year 2017 was marked by the Food and Drug Administration (FDA) approval of the first two chimeric antigen receptor-T (CAR-T) therapies. The approved indications were for the treatment of relapsed or refractory diffuse large B-cell lymphoma (DLBCL) and for the treatment of patients up to 25 years of age with acute lymphoblastic leukemia (ALL) that is refractory or in a second or later relapse. Since then, extensive research activities have been ongoing globally on different hematologic and solid tumors to assess the safety and efficacy of CAR-T therapy for these diseases. Limitations to CAR-T therapy became apparent from, e.g., the relapse in up to 60% of patients and certain side effects such as cytokine release syndrome (CRS). This led to extensive clinical activities aimed at overcoming these obstacles, so that the use of CAR-T therapy can be expanded. Attempts to improve on efficacy and safety include changing the CAR-T administration schedule, combining it with chemotherapy, and the development of next-generation CAR-T therapies, e.g., through the use of CAR-natural killer (CAR-NK) and CAR macrophages (CAR-Ms). This review will focus on new CAR-T treatment strategies in hematologic malignancies, clinical trials aimed at improving efficacy and addressing side effects, the challenges that CAR-T therapy faces in solid tumors, and the ongoing research aimed at overcoming these challenges.