There is growing interest in the possibility that genetic compatibility may drive mate choice, including gamete choice, particularly from the perspective of understanding why females frequently mate with more than one male. Mate choice for compatibility differs from other forms of choice for genetic benefits (such as 'good genes') because individuals are expected to differ in their mate preferences, changing the evolutionary dynamics of sexual selection. Recent experiments designed to investigate genetic benefits of polyandry suggest that mate choice on the basis of genetic compatibility may be widespread. However, in most systems the mechanisms responsible for variation in compatibility are unknown. We review potential sources of variation in genetic compatibility and whether there is any evidence for mate choice driven by these factors. Selfish genetic elements appear to have the potential to drive mate compatibility mate choice, though as yet there is only one convincing example. There is abundant evidence for assortative mating between populations in hybrid zones, but very few examples where this is clearly a result of selection against mating with genetically less compatible individuals. There are also numerous cases of inbreeding avoidance, but little evidence that mate choice or differential fertilization success driven by genetic compatibility occurs between unrelated individuals. The exceptions to this are a handful of situations where both the alleles causing incompatibility and the alleles involved in mate choice are located in a chromosome region where recombination is suppressed. As yet there are only a few potential sources of genetic compatibility which have clearly been shown to drive mate choice. This may reflect limitations in the potential for the evolution of mate choice for genetic compatibility within populations, although the most promising sources of such incompatibilities have received relatively little research.