In the past few years, chimeric antigen receptor (CAR) T-cell therapy has emerged as a promising treatment for cancers that failed standard treatments. Such therapies have already been approved in several blood cancers, such as B-cell leukemia and lymphoma. Despite this progress, a significant proportion of patients experience primary or secondary resistance to CAR T-cell therapy. Here, we review the mechanisms by which CAR T cells eliminate their target and how cancer cells may be insensitive to such killing (here referred to as intrinsic resistance). Recent studies suggest that the activation of apoptosis through death receptor signaling is responsible for a major part of CAR T-cell cytotoxicity in vivo. Indeed, cancer cells harboring aberrant apoptotic machinery may be insensitive to CAR T-cell killing. This intrinsic resistance of cancer cells to CAR T-cell killing could be responsible for a significant portion of treatment failure. Finally, we discuss strategies that may be envisioned to overcome such resistance to enhance CAR T-cell efficacy.