Viruses are considered as causative agents of a significant proportion of human cancers. While the very stringent criteria used for their classification probably lead to an underestimation, only six human viruses are currently classified as oncogenic. In this review we give a brief historical account of the discovery of oncogenic viruses and then analyse the mechanisms underlying the infectious causes of cancer. We discuss viral strategies that evolved to ensure virus propagation and spread can alter cellular homeostasis in a way that increases the probability of oncogenic transformation and acquisition of stem cell phenotype. We argue that a useful way of analysing the convergent characteristics of viral infection and cancer is to examine how viruses affect the so-called cancer hallmarks. This view of infectious origin of cancer is illustrated by examples from hepatitis C infection, which is associated with a high proportion of hepatocellular carcinoma.