The present monograph describes different ways to define the action of earthquakes upon structures. The progress that has taken place in recent years the application of different models to define the seismic action requires a panoramic view of the different existing methods. However, the literature on such methods is widely dispersed in different publications, and this publication brings together and synthesizes the most outstanding models. The fact that the seismic action has a a complex nature, and that frequently occur seismic events that exceed the forecasts, has maintained the traditional vocation of the Earthquake Engineering to collect and assimilate the new developments in fields as diverse as seismology, signal analysis, probability theory and stochastic processes, mechanics of materials, etc. Important developments have been achieved in the traditional model of response spectra, usual in the everyday design of simple structures, incorporating spectra based on seismological models, of damage indices or of energy. A wide range of algorithms for the simulation of accelerograms are also available, ranging from those that are limited to the compatibility with response spectra or with a seismological model to those that allow developing spatial models of the waves. Finally, an important development has taken place in relation to the stochastic modeling of the seismic action, which has made possible advances in the probabilistic methods of structural response and in the structural safety.