Human polyomaviruses show relatively little genetic polymorphism between isolates, indicating that these viruses are genetically stable between hosts. However, it has become increasingly clear that intra-host molecular evolution is a feature of some polyomavirus (PyV) infections in humans. Mutations inducing premature stop codons in the early region of the integrated Merkel cell PyV genome lead to the expression of a truncated form of the large tumour (LT) antigen that is critical for the transformation of Merkel cell carcinoma (MCC) cells. Non-coding control region (NCCR) rearrangements and point mutations in virion protein (VP) 1 have been described in both JCPyV and BKPyV infections. In the context of JCPyV infection, molecular evolution at both these loci allows the virus to replicate effectively in the central nervous system, thereby leading to the development of progressive multifocal leukoencephalopathy (PML). In BKPyV infection, NCCR rearrangements have been linked to higher rates of virus replication in the kidney, and are proposed to play a direct causal role in the development of PyV-associated nephropathy. In all three of these infections, therefore, intra-host viral evolution appears to be an essential component of the disease process. This article is part of the theme issue 'Silent cancer agents: multi-disciplinary modelling of human DNA oncoviruses'.