T cell malignancies pose several unique issues for CAR-T cell therapy that were not significant concerns with CAR-T cells for B-cell malignancies. A general problem to consider in the production of CAR-T cells is "on target-off tumor toxicity." This occurs when the antigen targeted by the CAR-T cells is also expressed on normal cells, not just tumor cells, which causes CAR-T cells to damage these normal cells. In CAR-T cell therapy for T cell tumors, antigens expressed on T cells (such as CD5, CD7, etc.) are the targets, which leads to a problem known as "fratricide," where CAR-T cells kill each other. Other issues include T cell aplasia and contamination of CAR-T cell products with tumor cells. However, several recent clinical trials have shown excellent outcomes for CAR-T cell therapy when genome editing technology is used to overcome these issues by knocking out target antigens or T cell receptors. This review article outlines these challenges and their solutions and discusses the results of recent clinical trials.