Assistive technology for the differently abled and older adults has made remarkable achievements in providing rehabilitative, adaptive, and assistive devices. It provides huge assistance for people with physical impairments to lead a better self-reliant daily life, in terms of mobility, education, rehabilitation, etc. This technology ranges from simple hand-held devices to complex robotic accessories which promote the individual's independence. This study aimed at identifying the assistance required by differently-abled individuals, and the solutions proposed by different researchers, and reviewed their merits and demerits. It provides a detailed discussion on the state of art assistive technologies, their applications, challenges, types, and their usage for rehabilitation. The study also identifies different unexplored research areas related to assistive technology that can improve the daily life of individuals and advance the field. Despite their high usage, assistive technologies have some limitations which have been briefly described in the study. This review, therefore, can help understand the utilization, and pros and cons of assistive devices in rehabilitation engineering and assistive technologies.