Robot dynamics has been traditionally viewed from the perspective of a manipulator's joint motions, and significant effort has been devoted to the development of joint space dynamic models and control methodologies. However, the limitations of joint space control techniques, especially in constrained motion tasks, have motivated alternative approaches for dealing with task-level dynamics and control. The operational space formulation, which falls within this line of research, has been driven by the need to develop mathematical models for the description, analysis, and control of robot dynamics with respect to task behavior. In this article, we review the operational space task-level models and discuss the various control methodologies that have been developed in this framework. These include : the unified motion and force control approach ; the notion of dynamic consistency in redundant manipulator control ; the reduced effective inertia property associated with macro-/mini-manipulator systems and the dextrous dynamic coordination strategy proposed for their control ; and the augmented-object model for the control of robot systems involving multiple manipulators.