Soft actuators and robotic devices have been increasingly applied to the field of rehabilitation and assistance, where safe human and machine interaction is of particular importance. Compared with their widely used rigid counterparts, soft actuators and robotic devices can provide a range of significant advantages; these include safe interaction, a range of complex motions, ease of fabrication and resilience to a variety of environments. In recent decades, significant effort has been invested in the development of soft rehabilitation and assistive devices for improving a range of medical treatments and quality of life. This review provides an overview of the current state-of-the-art in soft actuators and robotic devices for rehabilitation and assistance, in particular systems that achieve actuation by pneumatic and hydraulic fluid-power, electrical motors, chemical reactions and soft active materials such as dielectric elastomers, shape memory alloys, magnetoactive elastomers, liquid crystal elastomers and piezoelectric materials. Current research on soft rehabilitation and assistive devices is in its infancy, and new device designs and control strategies for improved performance and safe human-machine interaction are identified as particularly untapped areas of research. Finally, insights into future research directions are outlined.