In this chapter we discuss the control of underactuated mechanical systems. Underactuated mechanical systems have fewer control inputs than degrees of freedom and arise in applications, such as space and undersea robots, mobile robots, flexible robots, walking, branchiating, and gymnastic robots. The Lagrangian dynamics of these systems may contain feedforward nonlinearities, non-minimum phase zero dynamics, nonholonomic constraints, and other properties that place this class of systems at the forefront of research in nonlinear control [22, 15]. A complete understanding of the control of these systems is therefore lacking. We will discuss the application of geometric nonlinear control, as well as methods based on passivity and energy for stabilization and tracking control. We will survey some of the existing results and point to open research problems.