Human papillomavirus (HPV) infection is the most common sexually transmitted infection in the world. Persistent oncogenic Human papillomavirus infection has been a leading threat to global health and can lead to serious complications such as cervical cancer. Prevention interventions including vaccination and screening have been proved effective in reducing the risk of HPV-related diseases. In recent decades, computational epidemiology has been serving as a very useful tool to study HPV transmission dynamics and evaluation of prevention strategies. In this paper, we conduct a comprehensive literature review on state-of-the-art computational epidemic models for HPV disease dynamics, transmission dynamics, as well as prevention efforts. We summarise current research trends, identify gaps in the present literature, and identify future research directions with potential in accelerating the containment and/or elimination of HPV infection.