Impedance control is an approach to specify a desired second order dynamics during physical interactions with an envi-ronment, which compared to position and or force control makes the relations between the kinematic and kinetic varia-bles explicit. Further, compliance controllers do not specify a desired inertia, useful for achieving better robustness and stability properties. With respect to the task space definitions, it may be freely chosen under the condition that it has some kinematics mapping. As the tasks may not be of equal importance, a strict hierarchy can be enforced by modifying the robot jacobian with dynamically consistent nullspace projections. The resulting task space dynamics are inertially decoupled and do not permit task forces of lower priorities to disturb accelerations of higher priorities in a minimum-kinetic-energy sense. This general framework has been applied to diverse robots as well as extended upon in several works. This paper serves to summarize and give an overview of these recent developments.