Goats (Capra hircus) provide a rich source of products, such as meat, milk, and wool, and are important domestic animals in many parts of the world.  Goats were one of the first domesticated livestock species during the late Neolithic period, approximately 11,000 years ago, in the Fertile Crescent.  In the past decades, genomic studies of goats have provided insight into their domestication and genetic basis of economically important traits.  This review outlines the latest advancements that have been made in reference to domestication and genetic improvement of production traits such as meat and carcass quality, reproduction, milk, cashmere, and functional traits such as environmental adaptation and disease-resistance.  Genomic research is entering a new era with the availability of graphical pan-genomics and telomere-to-telomere (T2T) gap-free genome assembly, which will extend our understanding of domestication and molecular mechanistic dissection of economic traits in goats.  We provide new perspectives and future directions for genomics and suggest how the ever-increasing multi-omics dataset will facilitate future studies and molecular breeding in goat.