Motion generation for humanoid robots is a challenging task involving coordination, control, and stabilization of balance. This success was made possible by the systematic use of operational-space inverse dynamics (OSID) to compute dynamically consistent movements following a motion capture pattern demonstrated by a human choreographer. OSID can be seen as an extension of Inverse kinematics (IK) that deals with most of the limitations of IK. The idea of OSID is to define the motion to be executed by the robot in terms of reference movements in properly chosen operational spaces typically with a smaller dimension than that of the robot state space. The forward link between the state space and the operational space is given by the task function, whose image maps the operational space. This function is chosen so that the movement is easier to express in the operational space than in the state space. One of the major interests of OSID is to handle limited actuation systems. Humanoid robots, which are floating-based systems, are a particular case of underactuated systems due to the partial actuation that is completed when they make contact with the environment. OSID enforces actuation constraints, in particular contacts, which cannot be obtained with IK.