This paper deals with some fundamental considerations regarding the behaviour of geotechnical structures under seismic loading. First a complete definition of the earthquake disaster risk is provided, followed by the importance of performing site-specific hazard analysis. Then some suggestions are provided in regard to adequate assessment of soil parameters, a crucial point to properly analyze the seismic behaviour of geotechnical structures. The core of the paper is centered on a critical review of the analysis methods available for studying geotechnical structures under seismic loadings. All of the available methods can be classified into three main classes, including the pseudo-static, pseudo-dynamic and dynamic approaches, each of which is reviewed for applicability. A more advanced analysis procedure, suitable for a so-called performance-based design approach, is also described in the paper. Finally, the seismic behaviour of the El Infiernillo Dam was investigated. It was shown that coupled elastoplastic dynamic analyses disclose some of the important features of dam behaviour under seismic loading, confirmed by comparing analytical computation and experimental measurements on the dam body during and after a past earthquake.