This article is a review of the literature aimed at gaining a better understanding of the phenomena involved in belt drive systems. The numerous works on this subject (theory and experimentation) published over the last 2 centuries reveal three main approaches to the problem. In the first, the authors sought to determine the actual cause of the tension difference in the belt strands, through either friction or shear theory. The main objective was an attempt to explain the phenomena at work in the pulley/belt contact zone. Published work advocating the second approach aimed to solve the various equations of motion translating the excitation mechanisms of the belt’s transverse vibrations. This approach deliberately neglected the belt’s bending stiffness. The authors who proposed the latter approach investigated the equations of motion, as in the previous approach, but this time integrating the belt’s physical characteristics (bending stiffness, damping modes, thickness). This literature review finally shows that the various theoretical and experimental studies (notably with test benches) indicate that bending stiffness plays a non-negligible role in belt excitation and generates speed fluctuations at the crankshaft. The existence of this fluctuation results in the different vibratory modes to which the belt is subjected.