Some viruses are known to be associated with the onset of specific cancers. These microorganisms, oncogenic viruses or oncoviruses, can convert normal cells into cancer cells by modulating the central metabolic pathways or hampering genomic integrity mechanisms, consequently inhibiting the apoptotic machinery and/or enhancing cell proliferation. Seven oncogenic viruses are known to promote tumorigenesis in humans: human papillomavirus (HPV), hepatitis B and C viruses (HBV, HCV), Epstein-Barr virus (EBV), human T-cell leukemia virus 1 (HTLV-1), Kaposi sarcoma-associated herpesvirus (KSHV), and Merkel cell polyomavirus (MCPyV). Recent research indicates that SARS-CoV-2 infection and COVID-19 progression may predispose recovered patients to cancer onset and accelerate cancer development. This hypothesis is based on the growing evidence regarding the ability of SARS-CoV-2 to modulate oncogenic pathways, promoting chronic low-grade inflammation and causing tissue damage. Herein, we summarize the main relationships known to date between virus infection and cancer, providing a summary of the proposed biochemical mechanisms behind the cellular transformation. Mechanistically, DNA viruses (such as HPV, HBV, EBV, and MCPyV) encode their virus oncogenes. In contrast, RNA viruses (like HCV, HTLV-1) may encode oncogenes or trigger host oncogenes through cis-/-trans activation leading to different types of cancer. As for SARS-CoV-2, its role as an oncogenic virus seems to occur through the inhibition of oncosuppressors or controlling the metabolic and autophagy pathways in the infected cells. However, these effects could be significant in particular scenarios like those linked to severe COVID-19 or long COVID. On the other hand, looking at the SARS-CoV-2─cancer relationship from an opposite perspective, oncolytic effects and anti-tumor immune response were triggered by SARS-CoV-2 infection in some cases. In summary, our work aims to recall comprehensive attention from the scientific community to elucidate the effects of SARS-CoV-2 and, more in general, β-coronavirus infection on cancer susceptibility for cancer prevention or supporting therapeutic approaches.