Cancer research relies on model systems, which reflect the biology of actual human tumours to only a certain extent. One important feature of human cancer is its intra-tumour genomic heterogeneity and instability. However, the extent of such genomic instability in cancer models has received limited attention in research. Here, we review the state of knowledge of genomic instability of cancer models and discuss its biological origins and implications for basic research and for cancer precision medicine. We discuss strategies to cope with such genomic evolution and evaluate both the perils and the emerging opportunities associated with it.