Invited review: the application of runs of homozygosity and heterozygosity-rich regions to infer population history in livestock species

• ROH are valuable genomic tools for quantifying individual inbreeding and identifying regions under selection in livestock populations. • HRR are potentially maintained by balancing selection and linked to fitness-related traits, such as immunity and fertility. • Joint analysis of ROH and HRR enhances our understanding of genetic diversity patterns and supports the development of more sustainable breeding programs. • ROH and HRR have practical implications for managing inbreeding depression, maintaining adaptive genetic variation, and designing conservation strategies for local or endangered breeds. Advancements in high-throughput and cost-effective genotyping techniques, coupled with robust statistical methods, have greatly facilitated the investigation of the genomic architecture of farm animals. Runs of Homozygosity (ROH) and Heterozygosity-Rich Regions (HRR) are among the most informative features of animal genomes. ROH reflects inbreeding levels and historical population dynamics, whereas HRR may indicate loci under balancing selection that contribute to important functional traits. In this review, these two genetic parameters are described and discussed. We present an updated summary of ROH studies and applications in livestock species, as well as a comprehensive overview of the status of knowledge on HRR in livestock populations. Additionally, we discuss methods for the identification of ROH and HRR, and the insights they offer on the demographic history of animal species. We investigated the link between the presence, distribution, and specific characteristics of ROH and HRR, and the breeding and selection trajectories of farm animals. ROH- and HRR-abundant regions often harbour genes associated with economically important traits and local adaptation, underscoring the significant role of artificial and natural selection in shaping the genomic architecture of livestock. The increasing availability of high-density genotyping and whole-genome sequencing data allows for the finer-scale detection of ROH and HRR, enabling a more accurate identification of functionally relevant genomic regions. The future application of ROH and HRR in livestock genetics will likely move toward more integrated, data-driven strategies aimed at improving genetic resilience, productivity and sustainability.