Despite the impressive results of autologous CAR-T cell therapy in refractory B lymphoproliferative diseases, CAR-NK immunotherapy emerges as a safer, faster, and cost-effective approach with no signs of severe toxicities as described for CAR-T cells. Permanently scrutinized for its efficacy, recent promising data in CAR-NK clinical trials point out the achievement of deep, high-quality responses, thus confirming its potential clinical use. Although CAR-NK cell therapy is not significantly affected by the loss or downregulation of its CAR tumor target, as in the case of CAR-T cell, a plethora of common additional tumor intrinsic or extrinsic mechanisms that could also disable NK cell function have been described. Therefore, considering lessons learned from CAR-T cell therapy, the emergence of CAR-NK cell therapy resistance can also be envisioned. In this review we highlight the processes that could be involved in its development, focusing on cytokine addiction and potential fratricide during manufacturing, poor tumor trafficking, exhaustion within the tumor microenvironment (TME), and NK cell short in vivo persistence on account of the limited expansion, replicative senescence, and rejection by patient’s immune system after lymphodepletion recovery. Finally, we outline new actively explored alternatives to overcome these resistance mechanisms, with a special emphasis on CRISPR/Cas9 mediated genetic engineering approaches, a promising platform to optimize CAR-NK cell function to eradicate refractory cancers.