Abstract Characterizing the impact of genomic variants on genome function and ultimately complex traits in livestock is essential for the development of sustainable precision agriculture and comparative genomics. Here, as part of the Farm animal Genotype-Tissue Expression (FarmGTEx) project, we present the pilot phase of the SheepGTEx resource through analyzing 6,761 RNA-sequencing samples of 51 primary tissues in a multi-breed population of sheep. We identify millions of regulatory variants associated with seven types of molecular phenotypes, and fine-map 322,467 primary and 113,968 non-primary effects, revealing a high degree of regulatory allelic heterogeneity. We systematically characterize the pleiotropic effects of these variants on molecular phenotypes, assess their context-specific regulatory patterns across tissues, breeds, sexes, and developmental stages, as well as explore their evolutionary constraints across mammals. Finally, we demonstrate the substantial potential of the SheepGTEx resource ( https://sheepgtex.farmgtex.org ), by providing examples of regulatory mechanisms underpinning 34 complex traits, population divergence between European and Asian breeds, and adaptive evolution in sheep over the past ten millennia.