Human societies have been trying to mitigate the suffering of individuals with physical impairments, with a special effort in the last century. In the 1950s, a new concept arose, finding similarities between animal exoskeletons, and with the goal of medically aiding human movement (for rehabilitation applications). There have been several studies on using exosuits with this purpose in mind. So, the current review offers a critical perspective and a detailed analysis of the steps and key decisions involved in the conception of an exoskeleton. Choices such as design aspects, base materials (structure), actuators (force and motion), energy sources (actuation), and control systems will be discussed, pointing out their advantages and disadvantages. Moreover, examples of exosuits (full-body, upper-body, and lower-body devices) will be presented and described, including their use cases and outcomes. The future of exoskeletons as possible assisted movement solutions will be discussed-pointing to the best options for rehabilitation.