We review the underlying principles and tools used in genomic studies of domestic dogs aimed at understanding the genetic changes that have occurred during domestication. We show that there are two principle modes of evolution within dogs. One primary mode that accounts for much of the remarkable diversity of dog breeds is the fixation of discrete mutations of large effect in individual lineages that are then crossed to various breed groupings. This transfer of mutations across the dog evolutionary tree leads to the appearance of high phenotypic diversity that in actuality reflects a small number of major genes. A second mechanism causing diversification involves the selective breeding of dogs within distinct phenotypic or functional groups, which enhances specific group attributes such as heading or tracking. Such progressive selection leads to a distinct genetic structure in evolutionary trees such that functional and phenotypic groups cluster genetically. We trace the origin of the nuclear genome in dogs based on haplotype-sharing analyses between dogs and gray wolves and show that contrary to previous mtDNA analyses, the nuclear genome of dogs derives primarily from Middle Eastern or European wolves, a result more consistent with the archeological record. Sequencing analysis of the IGF1 gene, which has been the target of size selection in small breeds, further supports this conclusion. Finally, we discuss how a black coat color mutation that evolved in dogs has transformed North American gray wolf populations, providing a first example of a mutation that appeared under domestication and selectively swept through a wild relative.