Deletions and duplications of chromosomal segments (copy number variants, CNVs) are a major source of variation between individual humans and are an underlying factor in human evolution and in many diseases, including mental illness, developmental disorders and cancer. CNVs form at a faster rate than other types of mutation, and seem to do so by similar mechanisms in bacteria, yeast and humans. Here we review current models of the mechanisms that cause copy number variation. Non-homologous end-joining mechanisms are well known, but recent models focus on perturbation of DNA replication and replication of non-contiguous DNA segments. For example, cellular stress might induce repair of broken replication forks to switch from high-fidelity homologous recombination to non-homologous repair, thus promoting copy number change.