Soft robots with biological features have revolutionized their applications. The orientation and position of the upper limb joints can be emulated by carefully engineered soft materials. Due to their versatility and adaptability, these materials can imitate complex joint kinematics such as flexion and extension. The upper limb joints’ mobility permits human beings to perform basic and advanced tasks. There exists a lack of comprehensive studies that replicate the exact upper limb joint movements for use in different applications. This paper provides an overview of the recent breakthroughs in soft robots that clone the design and kinematics of the human upper limb joints. Studies have shown that it is possible to successfully achieve some degree of similarity between the proposed model and upper limb joints. Nevertheless, soft robotics is still an emerging field that requires more research on robust and biocompatible materials to be fully integrated for commercialization.