In this chapter, the concept of seismic risk is introduced and a review of its historical evolution is made. The number of seismic catastrophes has also been increasing in the twentieth century while the number of earthquakes with destructive capacity remains constant. This must be correlated with the growth of the world's population and with the increasing extension of urban areas in the seismic regions of the world. In these areas, coexist buildings designed by applying advanced standards, with old buildings, without any seismic design. There are also more and more catastrophes of another origin, related to storms, floods, droughts, effects of human activity on the environment, etc. It is very relevant that the increase in seismic risk occurs in the conditions in which seismic standards are continuously improving in all countries. Finally, the authors introduce the concept of seismic scenario and show examples of application for the city of Barcelona, Spain.