Abstract The alteration of wild populations has been discussed as a solution to a number of humanity’s most pressing ecological and public health concerns. Enabled by the recent revolution in genome editing, CRISPR gene drives, selfish genetic elements which can spread through populations even if they confer no advantage to their host organism, are rapidly emerging as the most promising approach. But before real-world applications are considered, it is imperative to develop a clear understanding of the outcomes of drive release in nature. Toward this aim, we mathematically study the evolutionary dynamics of CRISPR gene drives. We demonstrate that the emergence of drive-resistant alleles presents a major challenge to previously reported constructs, and we show that an alternative design which selects against resistant alleles greatly improves evolutionary stability. We discuss all results in the context of CRISPR technology and provide insights which inform the engineering of practical gene drive systems.