Adoptive immunotherapy that makes use of genetically modified autologous T cells carrying a chimeric antigen receptor (CAR) with desired specificity is a promising approach to the treatment of advanced or relapsed solid tumors. However, there are a number of challenges facing the CAR T-cell therapy, including the ability of the tumor to silence the expression of target antigens in response to the selective pressure exerted by therapy and the dampening of the functional activity of CAR T cells by the immunosuppressive tumor microenvironment. This review discusses the existing gene-engineering approaches to the modification of CAR T-cell design for 1) creating universal “switchable” synthetic receptors capable of attacking a variety of target antigens; 2) enhancing the functional activity of CAR T cells in the immunosuppressive microenvironment of the tumor by silencing the expression of inhibiting receptors or by stimulating production of cytokines.