Gorillas are humans’ closest living relatives after chimpanzees, and are of comparable importance for the study of human origins and evolution. Here we present the assembly and analysis of a genome sequence for the western lowland gorilla, and compare the whole genomes of all extant great ape genera. We propose a synthesis of genetic and fossil evidence consistent with placing the human–chimpanzee and human–chimpanzee–gorilla speciation events at approximately 6 and 10 million years ago. In 30% of the genome, gorilla is closer to human or chimpanzee than the latter are to each other; this is rarer around coding genes, indicating pervasive selection throughout great ape evolution, and has functional consequences in gene expression. A comparison of protein coding genes reveals approximately 500 genes showing accelerated evolution on each of the gorilla, human and chimpanzee lineages, and evidence for parallel acceleration, particularly of genes involved in hearing. We also compare the western and eastern gorilla species, estimating an average sequence divergence time 1.75 million years ago, but with evidence for more recent genetic exchange and a population bottleneck in the eastern species. The use of the genome sequence in these and future analyses will promote a deeper understanding of great ape biology and evolution.