High-risk human papillomaviruses (HPVs) are the main cause of cervical, oropharyngeal, and anogenital cancers, which are all treated with definitive chemoradiation therapy when locally advanced. HPV proteins are known to exploit the host DNA damage response to enable viral replication and the epithelial differentiation protocol. This has far-reaching consequences for the host genome, as the DNA damage response is critical for the maintenance of genomic stability. HPV+ cells therefore have increased DNA damage, leading to widespread genomic instability, a hallmark of cancer, which can contribute to tumorigenesis. Following transformation, high-risk HPV oncoproteins induce chromosomal instability, or chromosome missegregation during mitosis, which is associated with a further increase in DNA damage, particularly due to micronuclei and double-strand break formation. Thus, HPV induces significant DNA damage and activation of the DNA damage response in multiple contexts, which likely affects radiation sensitivity and efficacy. Here, we review how HPV activates the DNA damage response, how it induces chromosome missegregation and micronuclei formation, and discuss how these factors may affect radiation response. Understanding how HPV affects the DNA damage response in the context of radiation therapy may help determine potential mechanisms to improve therapeutic response.