Chimeric antigen receptor (CAR) technology, and CAR-T cells in particular, have emerged as a new and powerful tool in cancer immunotherapy since demonstrating efficacy against several hematological malignancies. However, despite encouraging clinical results of CAR-T cell therapy products, a significant proportion of patients do not achieve satisfactory responses, or relapse. In addition, CAR-T cell applications to solid tumors is still limited due to the tumor microenvironment and lack of specifically targetable tumor antigens. All current products on the market, as well as most investigational CAR-T cell therapies, are autologous, using the patient's own peripheral blood mononuclear cells as starting material to manufacture a patient-specific batch. Alternative cell sources are, therefore, under investigation (e.g. allogeneic cells from an at least partially human leukocyte antigen (HLA)-matched healthy donor, universal "third-party" cells from a non-HLA-matched donor, cord blood-derived cells, immortalized cell lines or cells differentiated from induced pluripotent stem cells). However, genetic modifications of CAR-engineered cells, bioprocesses used to expand cells, and improved supply chains are still complex and costly. To overcome drawbacks associated with CAR-T technologies, novel CAR designs have been used to genetically engineer cells derived from alpha beta (αβ) T cells, other immune cells such as natural killer (NK) cells, gamma delta (γδ) T cells, macrophages or dendritic cells. This review endeavours to trigger ideas on the next generation of CAR-engineered cell therapies beyond CAR-T cells and, thus, will enable effective, safe and affordable therapies for clinical management of cancer. To achieve this, we present a multidisciplinary overview, addressing a wide range of critical aspects: CAR design, development and manufacturing technologies, pharmacological concepts and clinical applications of CAR-engineered cell therapies. Each of these fields employs a large number of ground-breaking scientific advances, where coordinated and complex process and product development occur at their interfaces.