Historic urban centres are, almost by definition, risk-prone areas. The buildings in the historical sites are often highly vulnerable to natural and human-made hazards, not only due to their construction and material characteristics but also because they are usually very degraded due to ineffective maintenance and conservation policies. Moreover, the recent world tourism boom has led to a significant increase in the number of people who live, work and visit these areas, which, together with land use and climate change-related impacts, make historic centres particularly exposed areas. This paper addresses the issue of assessing and managing risk in historic urban centres departing from the complexity of defining the historic city and the concept of risk, providing a comprehensive discussion on current trends and future research directions in this field. After analysing the most suitable methodologies to assess the vulnerability of these areas to different hazards, the focus is on data collection and organisation-related issues and how the different vulnerability assessment outputs can be used to manage and mitigate risk. Vulnerability and loss scenarios, evacuation and emergency planning, and retrofit and cost-benefit analyses are some of the aspects addressed herein. This discussion includes some considerations on the accuracy of these approaches and aspects related to their calibration and validation, covering from empirical calibration models to advanced artificial Intelligence-based techniques.