This survey gives a short introduction to the today robot structure and problems of motion control and some remarks for future aspects of lightweight, high performance robots, that will include parts with non negligible flexibilities. How the modelling of this time variant elastic deformations, a substantial part of any control strategy, can principally be done is shown based on the recent literature.The quasistatic method uses substitutive springs to describe the elastic deformations at special locations. For the dynamic behaviour of vibrating flexible links FE-methods, a vibration mode or shape functions approach or other combined methods may be applied. The characteristics of the FE-methods are their advantage of a realistic modelling of complex shaped links but with the drow back of high evaluation time. The vibration mode methods need a special knowledge to select the right set of functions but lead to short evaluation time. Combined methods are also based on a fracturizing of the deformable elements into smaller units, whose elastic properties can be described more easily.The modelling of the elastic properties and an adequate control will be an essential basis for a future time and energy efficient robot performance.