Our aim was to consider interaction control problems from different viewpoints, primarily taking into account practical problems and needs. Basic strategies for controlling the interaction of a robot with the environment are the subject of the paper. The paper also provides a historical perspective on interaction control, summarizing the major achievements in this area for the last 25 years. After this long period of investigation we are now faced with an inevitable change of generation in this field. Many young enthusiastic researchers are focusing now on various attractive issues in human-robot-environment interaction control, especially from the viewpoint of novel disciplines such as artificial intelligence, mechatronics, augmented reality, etc. Considering more complex tasks, the application of force sensors and interaction control techniques is certainly not sufficient to provide the robot with a required degree of autonomy and intelligence. The paper attempts to provide unified theoretical force and position control paradigms considering basic control issues: stability, performance, and robustness. This framework assumes a general dynamic environment and uses an inverse dynamic control strategy to design various controllers for specific force and position stabilization tasks. Stability problems during the dynamic control tasks are also considered in the paper using different stability criteria. The established contact stability theory has been expanded to the control and synthesis. Therefore, one of the basic characteristics of regular bipedal walk of humanoid robots is the maintenance of their dynamic balance during the walk, whereby a decisive role is played by the unpowered degrees of freedom arising at the foot-ground contact. Hence, the role of Zero-Moment Point (ZMP) as an indicator of dynamic balance is indispensable. On the other hand, we are witnesses of the diverse realizations of locomotion systems, from those with human-like feet, aiming to mimic in full the human gait, passive walkers, which practically roll on specially profiled feet, to the footless locomotion systems. It is quite clear that any of these systems can realize a gait (very often such gait is not dynamically balanced), but our present study shows that the performances of such walking systems are essentially different and inapt to meet the requirements that are stated for the humanoids in a human environment. This study points out the indispensability of the regular, fully dynamically balanced gait for the simultaneous realization of locomotion-manipulation activities, as well as for the walk in an unstructured environment.