Papillomaviruses dysregulate the G1/S cell cycle transition in order to promote DNA synthesis in S phase, which is a requirement for viral replication. The human papillomaviruses (HPV) E6 and E7 oncoproteins mediate degradation of the cell cycle regulators p53 and Rb, which are two of the most universally disrupted tumor-suppressor genes in all of cancer. The G1/S checkpoint is activated in normal cells to allow sufficient time for DNA repair in G1 before proceeding to replicate DNA and risk propagating unrepaired errors. The TP53 pathway suppresses a variety of such errors, including translocation, copy number alterations, and aneuploidy, which are thus found in HPV-associated tumors similarly to HPV-negative tumors with other mechanisms of TP53 disruption. However, E6 and E7 maintain a variety of other virus–host interactions that directly disrupt a growing list of other DNA repair and chromatin remodeling factors, implying HPV-specific repair deficiencies. In addition, HPV-associated squamous cell carcinomas tumors clinically respond differently to DNA damaging agents compared to their HPV negative counterparts. The focus of this review is to integrate three categories of observations: (1) pre-clinical understanding as to the effect of HPV on DNA repair, (2) genomic signatures of DNA repair in HPV-associated tumor genomes, and (3) clinical responses of HPV-associated tumors to DNA damaging agents. The goals are to try to explain why HPV-associated tumors respond so well to DNA damaging agents, identify missing pieces, and suggest clinical strategies could be used to further improve treatment of these cancers.