Livestock radiated out from domestication centres to most regions of the world, gradually adapting to diverse environments, from very hot to sub-zero temperatures and from wet and humid conditions to deserts. The climate is changing; generally global temperature is increasing, although there are also more extreme cold periods, storms, and higher solar radiation. These changes impact livestock welfare and productivity. This review describes advances in the methodology for studying livestock genomes and the impact of the environment on animal production, giving examples of discoveries made. Sequencing livestock genomes has facilitated genome-wide association studies to localize genes controlling many traits, and population genetics has identified genomic regions under selection or introgressed from one breed into another to improve production or facilitate adaptation. Landscape genomics, which combines global positioning and genomics, has identified genomic features that enable animals to adapt to local environments. Combining the advances in genomics and methods for predicting changes in climate is generating an explosion of data which calls for innovations in the way big data sets are treated. Artificial intelligence and machine learning are now being used to study the interactions between the genome and the environment to identify historic effects on the genome and to model future scenarios.