Wearables robots have gained attention for the rehabilitation of people with physical disabilities. However, the current technology relies on heavy and bulky actuation components, making it hard to use outside clinical settings. Artificial muscles based on smart materials are trending for soft wearable rehabilitation robots as they present advantages of compliance, are lightweight, and do not require external components. Nevertheless, they present challenges that remain unresolved, preventing widespread adoption. This work reviews the current state of soft wearable rehabilitation robots with artificial muscles based on smart materials (AMSMs). A literature search is conducted utilizing Web of Science and Scopus. Based on the inclusion–exclusion criteria, 15 devices are found using four different smart materials. This study attempts to provide an insight into the distinct biomechanical requirements, the use of smart materials, their limitations, their designs, and possible future research directions, which can provide helpful guidance on the implementation and development of advanced soft wearable rehabilitation robots with AMSMs.