Animal genomics is currently undergoing dynamic development, which is driven by the flourishing of high-throughput genome analysis methods. Recently, a large number of animals has been genotyped with the use of whole-genome genotyping assays in the course of genomic selection programmes. The results of such genotyping can also be used for studies on different aspects of livestock genome functioning and diversity. In this article, we review the recent literature concentrating on various aspects of animal genomics, including studies on linkage disequilibrium, runs of homozygosity, selection signatures, copy number variation and genetic differentiation of animal populations. Our work is aimed at providing insight into certain achievements of animal genomics and to arouse interest in basic research on the complexity and structure of the genomes of livestock.