Exoskeletons and orthoses are wearable mobile systems providing mechanical benefits to the users. Despite significant improvements in the last decades, the technology is not fully mature to be adopted for strenuous and non-programmed tasks. To accommodate this insufficiency, different aspects of this technology need to be analysed and improved. Numerous studies have tried to address some aspects of exoskeletons, e.g. mechanism design, intent prediction, and control scheme. However, most works have focused on a specific element of design or application without providing a comprehensive review framework. This study aims to analyse and survey the contributing aspects to this technology's improvement and broad adoption. To address this, after introducing assistive devices and exoskeletons, the main design criteria will be investigated from both physical Human-Robot Interaction (HRI) perspectives. In order to establish an intelligent HRI strategy and enable intuitive control for users, cognitive HRI will be investigated after a brief introduction to various approaches to their control strategies. The study will be further developed by outlining several examples of known assistive devices in different categories. And some guidelines for exoskeleton selection and possible mitigation of current limitations will be discussed.