The Darwin theory of evolution by natural selection is based on three principles: (a) variation; (b) inheritance; and (c) natural selection. Here, I take these principles as an excuse to review some topics related to the future research prospects in Animal Breeding. With respect to the first principle I describe two forms of variation different from mutation that are becoming increasingly important: variation in copy number and microRNAs. With respect to the second principle I comment on the possible relevance of non-mendelian inheritance, the so-called epigenetic effects, of which the genomic imprinting is the best characterized in domestic species. Regarding selection principle I emphasize the importance of selection for social traits and how this could contribute to both productivity and animal welfare. Finally, I analyse the impact of molecular biology in Animal Breeding, the achievements and limitations of quantitative trait locus and classical marker-assisted selection and the future of genomic selection.