With the recent progress in personal care robots, interest in wearable exoskeletons has been increasing due to the demand for assistive technologies generally and specifically to meet the concerns in the increasing ageing society. Despite this global trend, research focus has been on load augmentation for soldiers/workers, assisting trauma patients, paraplegics, spinal cord injured persons and for rehabilitation purposes. Barring the military-focused activities, most of the work to date has focused on medical applications. However, there is a need to shift attention towards the growing needs of elderly people, that is, by realizing assistive exoskeletons that can help them to stay independent and maintain a good quality of life. Therefore, the present article covers the rapidly evolving area of wearable exoskeletons in a holistic manner, for both medical and non-medical applications, so that relevant current developments and future issues can be addressed; this includes how the physical assistance/rehabilitation/compensation can be provided to supplement capabilities in a natural manner. Regulatory guidelines, important for realizing new markets for these emerging technologies, are also explored in this work. For these, emerging international safety requirements are presented for non-medical and medical exoskeleton applications, so that the central requirement of close human-robot interactions can be adequately addressed for the intended tasks to be carried out. An example case study on developing and commercializing wearable exoskeletons to help support living activities of healthy elderly persons is presented to highlight the main issues in non-medical mobility exoskeletons. This also paves the way for the potential future trends to use exoskeletons as physical assistant robots, as covered by the recently published safety standard ISO 13482, to help elderly people perform their activities of daily living.