Gene drives based on CRISPR/Cas9 have the potential to reduce the enormous harm inflicted by crop pests and insect vectors of human disease, as well as to bolster valued species. In contrast with extensive empirical and theoretical studies in diploid organisms, little is known about CRISPR gene drive in haplodiploids, despite their immense global impacts as pollinators, pests, natural enemies of pests, and invasive species in native habitats. Here, we analyze mathematical models demonstrating that, in principle, CRISPR homing gene drive can work in haplodiploids, as well as at sex-linked loci in diploids. However, relative to diploids, conditions favoring the spread of alleles deleterious to haplodiploid pests by CRISPR gene drive are narrower, the spread is slower, and resistance to the drive evolves faster. By contrast, the spread of alleles that impose little fitness cost or boost fitness was not greatly hindered in haplodiploids relative to diploids. Therefore, altering traits to minimize damage caused by harmful haplodiploids, such as interfering with transmission of plant pathogens, may be more likely to succeed than control efforts based on introducing traits that reduce pest fitness. Enhancing fitness of beneficial haplodiploids with CRISPR gene drive is also promising.