The genetic bases of demographic changes and artificial selection underlying domestication are of great interest in evolutionary biology. Here we perform whole-genome sequencing of multiple grey wolves, Chinese indigenous dogs and dogs of diverse breeds. Demographic analysis show that the split between wolves and Chinese indigenous dogs occurred 32,000 years ago and that the subsequent bottlenecks were mild. Therefore, dogs may have been under human selection over a much longer time than previously concluded, based on molecular data, perhaps by initially scavenging with humans. Population genetic analysis identifies a list of genes under positive selection during domestication, which overlaps extensively with the corresponding list of positively selected genes in humans. Parallel evolution is most apparent in genes for digestion and metabolism, neurological process and cancer. Our study, for the first time, draws together humans and dogs in their recent genomic evolution.