Social interactions, especially those involving competition among individuals, are important in domesticated livestock and in natural populations. The heritability of traits affected by such interactions has two components, one originating in the individual like that of classical traits (direct effects) and the other originating in other group members (indirect effects). The latter type of trait represents a significant source of ‘hidden heritability’ and it requires population structure and knowledge from relatives in order to access it for selective breeding. When ignored, competitive interactions may increase as an indirect response to direct selection, resulting in diminished yields. We illustrate how population genetic structure affects the response to selection of traits with indirect genetic effects using population genetic and quantitative genetic theory. Population genetic theory permits us to connect our results to the existing body of theory on kin and group selection in natural populations. The quantitative genetic perspective allows us to see how breeders have used knowledge from relatives and family selection in the domestication of plants and animals to improve the welfare and production of livestock by incorporating social genetic effects in the breeding program. We illustrate the central features of these models by reviewing empirical studies from domesticated chickens.