Apes possess two sex chromosomes-the male-specific Y and the X shared by males and females. The Y chromosome is crucial for male reproduction, with deletions linked to infertility. The X chromosome carries genes vital for reproduction and cognition. Variation in mating patterns and brain function among great apes suggests corresponding differences in their sex chromosome structure and evolution. However, due to their highly repetitive nature and incomplete reference assemblies, ape sex chromosomes have been challenging to study. Here, using the state-of-the-art experimental and computational methods developed for the telomere-to-telomere (T2T) human genome, we produced gapless, complete assemblies of the X and Y chromosomes for five great apes (chimpanzee, bonobo, gorilla, Bornean and Sumatran orangutans) and a lesser ape, the siamang gibbon. These assemblies completely resolved ampliconic, palindromic, and satellite sequences, including the entire centromeres, allowing us to untangle the intricacies of ape sex chromosome evolution. We found that, compared to the X, ape Y chromosomes vary greatly in size and have low alignability and high levels of structural rearrangements. This divergence on the Y arises from the accumulation of lineage-specific ampliconic regions and palindromes (which are shared more broadly among species on the X) and from the abundance of transposable elements and satellites (which have a lower representation on the X). Our analysis of Y chromosome genes revealed lineage-specific expansions of multi-copy gene families and signatures of purifying selection. In summary, the Y exhibits dynamic evolution, while the X is more stable. Finally, mapping short-read sequencing data from >100 great ape individuals revealed the patterns of diversity and selection on their sex chromosomes, demonstrating the utility of these reference assemblies for studies of great ape evolution. These complete sex chromosome assemblies are expected to further inform conservation genetics of nonhuman apes, all of which are endangered species.