Whether and how human tumours are genetically unstable has been debated for decades. There is now evidence that most cancers may indeed be genetically unstable, but that the instability exists at two distinct levels. In a small subset of tumours, the instability is observed at the nucleotide level and results in base substitutions or deletions or insertions of a few nucleotides. In most other cancers, the instability is observed at the chromosome level, resulting in losses and gains of whole chromosomes or large portions thereof. Recognition and comparison of these instabilities are leading to new insights into tumour pathogenesis.