Most traits of economic importance in livestock are either quantitative or complex. Despite considerable efforts, there has been only limited success in identifying the polymorphisms that cause variation in these traits. Nevertheless, selection based on estimated breeding values (BVs), calculated from data on phenotypic performance and pedigree has been very successful. Genomic tools, such as single nucleotide polymorphism (SNP) chips, have led to a new method of selection called 'genomic selection' in which dense SNP genotypes covering the genome are used to predict the BV. In this review we consider the statistical methodology for estimating BVs from SNP data, factors affecting the accuracy, the long-term response to genomic selection and the design of breeding programmes including the management of inbreeding.