Human papillomaviruses (HPVs) are the necessary cause of most cervical cancers, a large proportion of other anogenital cancers, and a subset of oropharyngeal cancers. The knowledge about HPV has led to development of novel HPV-based prevention strategies with important impact on clinical and public health practice. Two complementary reviews have been prepared following the 2015 Eurogin Conference to evaluate how knowledge about HPV is changing practice in HPV infection and disease control through vaccination and screening. This review focuses on screening for cervical and anal cancers in increasingly vaccinated populations. The introduction of HPV vaccines a decade ago has led to reductions in HPV infections and early cancer precursors in countries with wide vaccination coverage. Despite the high efficacy of HPV vaccines, cervical cancer screening will remain important for many decades. Many healthcare systems are considering switching to primary HPV screening, which has higher sensitivity for cervical precancers and allows extending screening intervals. We describe different approaches to implementing HPV-based screening efforts in different healthcare systems with a focus in high-income countries. While the population prevalence for other anogenital cancers is too low for population-based screening, anal cancer incidence is very high in HIV-infected men who have sex with men, warranting consideration of early detection approaches. We summarize the current evidence on HPV-based prevention of anal cancers and highlight important evidence gaps.