All over the world, several dozen million people suffer from the effects of post-polio, multiple sclerosis, spinal cord injury, cerebral palsy, etc. and could benefit from the advances in robotic devices for rehabilitation. Thus, for modern society, an important and vital problem of designing systems for rehabilitation of human physical working ability appears. The temporary or permanent loss of human motor functions can be compensated by means of various rehabilitation devices. They can be simple mechanical systems for orthoses, which duplicate the functions of human extremities supplying with rigidity and bearing capacity or more complex mechatronic rehabilitation devices with higher level of control. We attempt to cover all of the major developments in these areas, focusing particularly on the development of the different concepts and their functional characteristics. The robotic devices with several structures are classified, taking into account the actuation systems, the neuromuscular stimulations, and the structural schemes. It is showed that the problems concerning the design of rehabilitation devices are complex and involve many questions in the sphere of biomedicine, mechanics, robot technology, electromechanics and optimal control. This paper provides a design overview of hardware, actuation, sensory, and control systems for most of the devices that have been described in the literature, and it ends with a discussion of the major advances that have been made and should be yet overcome.