Incomplete lineage sorting (ILS) causes the phylogeny of some parts of the genome to differ from the species tree. In this work, we investigate the frequencies and determinants of ILS in 29 major ancestral nodes across the entire primate phylogeny. We find up to 64% of the genome affected by ILS at individual nodes. We exploit ILS to reconstruct speciation times and ancestral population sizes. Estimated speciation times are much more recent than genomic divergence times and are in good agreement with the fossil record. We show extensive variation of ILS along the genome, mainly driven by recombination but also by the distance to genes, highlighting a major impact of selection on variation along the genome. In many nodes, ILS is reduced more on the X chromosome compared with autosomes than expected under neutrality, which suggests higher impacts of natural selection on the X chromosome. Finally, we show an excess of ILS in genes with immune functions and a deficit of ILS in housekeeping genes. The extensive ILS in primates discovered in this study provides insights into the speciation times, ancestral population sizes, and patterns of natural selection that shape primate evolution.