In pig and poultry breeding programs, animals from genetically distinct purebred breeding lines are mated to produce crossbred animals, which provide food products to consumers. Although the aim of such breeding programs is to improve the performance of the crossbreds, selection takes place in the purebred lines, and is usually based on purebred performance. This strategy may be suboptimal because the genetic correlation between purebred and crossbred performance (r_pc) is usually lower than one. When r_pc is lower than one, it may be beneficial to make selection decisions based on information on crossbred performance instead of purebred performance. This is, however, a challenging task, because purebred animals cannot be tested directly for performance at the crossbred level. Now, with the recent developments in genomic prediction, it has become possible to estimate breeding values for crossbred performance of purebred animals. In this thesis, I studied the genetics of crossbreeding, with a focus on genomic prediction for crossbred performance in purebred lines. First, I illustrate how interactions between genes can lead to differences in genetic trait expression between lines, and how such interactions can lead to r_pc values that are lower than one. The results show that r_pc decreases as the genetic distance between parental lines increases. I derive expressions for r_pc based on genetic parameters in the parental lines, which allows breeders to estimate bounds of r_pc without having to collect crossbred data. Second, I show that genotype-based models lead to larger estimated r_pc with smaller standard errors than pedigree-based models. In contrast to my expectation, considering breed-of-origin of alleles in genotype-based models does not yield different estimates of r_pc. Third, I investigate the benefit of training the genomic prediction model with crossbred instead of purebred data. The results show that crossbred data improves the accuracy of breeding values for a trait with an r_pc of 0.8, but not for a trait with an r_pc of 0.96. Furthermore, taking the breed-of-origin of alleles into account is beneficial for a trait with an of 0.8, but not for a trait with an of 0.96. Finally, I discuss the relationship between r_pc and heterosis in the presence of gene interactions, and strategies to estimate breeding values for crossbred performance of purebreds. The results in this thesis improve our understanding of the genetics of crossbreeding, and facilitate the optimization of breeding programs that aim to improve crossbred performance with selection in purebred breeding lines.