An underactuated mechanical system (UMS) is the system that has fewer independent control actuators than degrees of freedom to be controlled. Control of UMS is considered as one of the most active fields of research due to its diverse engineering applications.This survey reviews UMS from its history to the state-of-the-art research on modelling, classification, control methods, and to some extent, provides some unique insights for bottleneck issues of control and future research directions.