Despite two decades of research into over one hundred species, the function of extrapair paternity to female birds remains unclear. Recent studies have demonstrated patterns between extrapair paternity and the genetic similarity of females with social partners and extrapair males. We believe that selection on females to gain genetically compatible fathers for their offspring offers a possible general explanation for the function of extrapair paternity. The idea of sexual selection being driven by genetic compatibility is widely considered by workers on other taxa but has been largely ignored by studies of birds. Genetic compatibility could be optimised by females through a behavioural process before copulation or through a postcopulatory process. Postcopulatory processes such as cryptic female choice have been recently demonstrated in birds and would allow female birds to use a 'genetically loaded raffle' to target compatible genes through sperm competition. We discuss the general weaknesses of studies of extrapair paternity to date and suggest a number of avenues for future research that will help to elucidate the function of extrapair paternity and widespread genetic polyandry in birds.