A functioning gene drive system could fundamentally change our strategies for the control of vector-borne diseases by facilitating rapid dissemination of transgenes that prevent pathogen transmission or reduce vector capacity. CRISPR/Cas9 gene drive promises such a mechanism, which works by converting cells that are heterozygous for a drive construct into homozygotes, thereby enabling super-Mendelian inheritance. Though CRISPR gene drive activity has already been demonstrated, a key obstacle for current systems is their propensity to generate resistance alleles. I will present both theoretical and experimental results that shed light on how such resistance alleles emerge during the drive process, how genetic variability in the population impacts their formation rate, and how these alleles are expected to ultimately affect the spread of a drive in the population. We find that the key factor determining the probability that resistance evolves is the formation rate of resistance alleles, while the conversion efficiency of the drive construct, its fitness cost, and its introduction frequency have only minor impact. Our experiments in the model system Drosophila melanogaster confirm that resistance alleles arise at high rates both prior to fertilization in the germline and post-fertilization in the embryo due to maternally deposited Cas9. These findings demonstrate that resistance will likely impose a severe limitation to the effectiveness of current CRISPR gene drive approaches, inform strategies for the engineering of drives with lower resistance potential, and motivate the possibility to embrace resistance as a possible mechanism for controlling a drive.