Vibrational spectroscopy is one of the most important experimental techniques for the characterization of molecules and materials. Spectroscopic signatures retrieved in experiments are not always easy to explain in terms of the structure and dynamics of the studied samples. Computational studies are a crucial tool for helping to understand and predict experimental results. Molecular dynamics simulations have emerged as an attractive method for the simulation of vibrational spectra because they explicitly treat the vibrational motion present in the compound under study, in particular in large and condensed systems, subject to complex intramolecular and intermolecular interactions. In this context, first-principles molecular dynamics (FPMD) has been proven to provide an accurate realistic description of many compounds. This review article summarizes the field of vibrational spectroscopy by means of FPDM and highlights recent advances made such as the simulation of Infrared, vibrational circular dichroism, Raman, Raman optical activity, sum frequency generation, and nonlinear spectroscopies.