Human oncogenic viruses are defined as necessary but not sufficient to initiate cancer. Experimental evidence suggests that the oncogenic potential of a virus is effective in cells that have already accumulated a number of genetic mutations leading to cell cycle deregulation. Current models for viral driven oncogenesis cannot explain why tumor development in carriers of tumorigenic viruses is a very rare event, occurring decades after virus infection. Considering that viruses are mutagenic agents per se and human oncogenic viruses additionally establish latent and persistent infections, we attempt here to provide a general mechanism of tumor initiation both for RNA and DNA viruses, suggesting viruses could be both necessary and sufficient in triggering human tumorigenesis initiation. Upon reviewing emerging evidence on the ability of viruses to induce DNA damage while subverting the DNA damage response and inducing epigenetic disturbance in the infected cell, we hypothesize a general, albeit inefficient hit and rest mechanism by which viruses may produce a limited reservoir of cells harboring permanent damage that would be initiated when the virus first hits the cell, before latency is established. Cells surviving virus generated damage would consequently become more sensitive to further damage mediated by the otherwise insufficient transforming activity of virus products expressed in latency, or upon episodic reactivations (viral persistence). Cells with a combination of genetic and epigenetic damage leading to a cancerous phenotype would emerge very rarely, as the probability of such an occurrence would be dependent on severity and frequency of consecutive hit and rest cycles due to viral reinfections and reactivations