In this research paper, we present a comprehensive analysis of the current state of soft robots actuated with pneumatic artificial muscles and emphasise their distinct advantages over rigid robots, including exceptional flexibility, adaptability, and safety. Our study explores the design principles of soft robots, drawing inspiration from biological systems and human hands, and identifies promising avenues for further development. The emergence of hybrid robots is also recognised as a significant advancement, particularly in scenarios requiring high precision. The article explores mathematical models encompassing kinematics, dynamics, and statics, as well as alternative model-free approaches. These theoretical frameworks are instrumental in understanding and manipulating the behaviour of soft robots. However, despite substantial progress, soft robots’ practical application and simulation face limitations, primarily due to the demanding requirements and implementation challenges associated with their deployment. Consequently, this paper highlights the need for continued research and advancements to bridge the gap between the theoretical potential and practical utilisation of soft robots.