Advances in genome sequencing technologies have created new opportunities for comparative primate genomics. Genome assemblies have been published for various primate species, and analyses of several others are underway. Whole-genome assemblies for the great apes provide remarkable new information about the evolutionary origins of the human genome and the processes involved. Genomic data for macaques and other non-human primates offer valuable insights into genetic similarities and differences among species that are used as models for disease-related research. This Review summarizes current knowledge regarding primate genome content and dynamics, and proposes a series of goals for the near future.