Structural dynamics has been the foundation of earthquake engineering following the developments made in the field since the 1940 El Centro earthquake in California. This event for which the ground motions were recorded by accelerometers and were further processed to yield spectra that marked the onset of modern studies in the field [1]. In essence, the lateral vibrations caused by ground motion to be analyzed by modelling the structure as an SDOF system, followed by MDOF representations a culminating in the use of the Finite Element Method (FEM). Furthermore, modal analysis was introduced followed by the use of response spectra for the analysis as well as for the design of structures. Furthermore, spectral methods (i.e., the use of the Fourier transform so that the dependent variable of the problem are now functions of frequency) were introduced, especially for random vibration studies given the stochastic nature of ground motions. In this chapter, an overview of all these topics will be given followed by some examples.