In the first part the paper outlines the current conceptions relevant to seismic risk for constructions in urban centres analysing seismic hazard, vulnerability and exposure. In the second part there are some details about the vulnerability assessment of ordinary buildings, and about the differences that arise when monumental or historical buildings are in question. Then the concept of seismic scenario is given (third part), so that the specific question of seismic vulnerability of historical centres may be treated (part four), presenting an appropriate methodology recently proposed by the author. Finally part five presents an introduction to the theme of risk mitigation for historical centres and monuments, a very difficult question, where the two aspects of preservation and seismic safety must be considered together.