Inverse dynamics problems arise in several mechanical systems. The aim is to calculate the inputs of a system in order that the outputs are identical to predefined or measured target signals. The motivation for inverse methods is related to practical applications in robotics, cranes or test rigs in the automotive and agricultural industry. The book considers four mathematical methods regarding to inverse problems in underactuated multibody systems. The first method under consideration is called virtual iteration. The algorithm is suitable for large multibody systems and finite element models, which are nearly linear. The second approach formulates the equations of motion as differential-algebraic equations and introduces so called control or servo constraints. The inverse problem can also be formulated as an optimal control problem. The basis is a cost functional, which includes the system outputs and the targets. The fourth method is a flatness-based trajectory tracking control. The considered methods are applied to academic and industrial examples.