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Traditional marker-assisted selection (MAS) did not result in a widespread use of DNA information in animal breeding. The main reason was that the traits of interest in livestock production were much more complex than expected: they were determined by thousands of genes with small effects on phenotype. These effects were usually too small to be statistically significant and so were ignored. Genomic selection (GS) assumes that all markers might be linked to a gene affecting the trait and concentrates on estimating their effect rather than testing its significance. Three technological breakthroughs resulted in the current wide-spread use of DNA information in animal breeding: the development of the genomic selection technology, the discovery of massive numbers of genetic markers (single nucleotide polymorphisms; SNPs), and high-throughput technology to genotype animals for (hundreds of) thousands of SNPs in a cost-effective manner. Here we review current methods for GS, including how they deal with practical data, where genotypes are missing on a large scale. The use of whole-genome sequence data is anticipated, and its advantages and disadvantages are depicted. Current and predicted future impacts of GS on dairy and beef cattle, pigs, and poultry breeding are described. Finally, future directions for GS are discussed. It is anticipated that future GS applications will either be: within breed (wbGS), where accuracy is obtained by maintaining huge within-breed reference populations; or across breed (abGS) where accuracy is obtained from across-breed reference populations and high-density GS methods that focus on causative genomic regions. We argue that future GS applications will increasingly turn toward abGS.