The great apes (orangutans, gorillas, chimpanzees, bonobos and humans) descended from a common ancestor around 13 million years ago, and since then their sex chromosomes have followed very different evolutionary paths. While great-ape X chromosomes are highly conserved, their Y chromosomes, reflecting the general lability and degeneration of this male-specific part of the genome since its early mammalian origin, have evolved rapidly both between and within species. Understanding great-ape Y chromosome structure, gene content and diversity would provide a valuable evolutionary context for the human Y, and would also illuminate sex-biased behaviours, and the effects of the evolutionary pressures exerted by different mating strategies on this male-specific part of the genome. High-quality Y-chromosome sequences are available for human and chimpanzee (and low-quality for gorilla). The chromosomes differ in size, sequence organisation and content, and while retaining a relatively stable set of ancestral single-copy genes, show considerable variation in content and copy number of ampliconic multi-copy genes. Studies of Y-chromosome diversity in other great apes are relatively undeveloped compared to those in humans, but have nevertheless provided insights into speciation, dispersal, and mating patterns. Future studies, including data from larger sample sizes of wild-born and geographically well-defined individuals, and full Y-chromosome sequences from bonobos, gorillas and orangutans, promise to further our understanding of population histories, male-biased behaviours, mutation processes, and the functions of Y-chromosomal genes.