Social interactions between individuals living in a group can have both positive and negative effects on welfare, productivity, and health of these individuals. Negative effects of social interactions in livestock are easier to observe than positive effects. For example, laying hens may develop feather pecking, which can cause mortality due to cannibalism, and pigs may develop tail biting or excessive aggression. Several studies have shown that social interactions affect the genetic variation in a trait. Genetic improvement of socially-affected traits, however, has proven to be difficult until relatively recently. The use of classical selection methods, like individual selection, may result in selection responses opposite to expected, because these methods neglect the effect of an individual on its group mates (social genetic effects). It has become clear that improvement of socially-affected traits requires selection methods that take into account not only the direct effect of an individual on its own phenotype but also the social genetic effects, also known as indirect genetic effects, of an individual on the phenotypes of its group mates. Here, we review the theoretical and empirical work on social genetic effects, with a focus on livestock. First, we present the theory of social genetic effects. Subsequently, we evaluate the evidence for social genetic effects in livestock and other species, by reviewing estimates of genetic parameters for direct and social genetic effects. Then we describe the results of different selection experiments. Finally, we discuss issues concerning the implementation of social genetic effects in livestock breeding programs. This review demonstrates that selection for socially-affected traits, using methods that target both the direct and social genetic effects, is a promising, but sometimes difficult to use in practice, tool to simultaneously improve production and welfare in livestock.