Pneumatic artificial muscles (PAMs) are soft and flexible linear pneumatic actuators which produce human muscle like actuation. Due to these properties, the muscle actuators have an adaptable compliance for various robotic platforms as well as medical applications. While a variety of possible actuation schemes are present, there is still a need for the development of a soft actuator that is very light-weight, compact, and flexible with high power-to-weight ratio. To achieve this, the development of the PAM actuators has become an interesting topic for many researchers. In this review, the development of the different kinds of PAM available to date are presented along with manufacturing process and the operating principle. The various force models for artificial muscle presented in the literature are broadly reviewed with the constraints. Furthermore, the applications of PAM are included and classified based on the fields of biorobotics, medicine, and industry, along with advanced medical instrumentation. Finally, the needful improvements in terms of the dynamics of the muscle are discussed for the precise control of the PAMs as per the requirements for the applications. This review will be helpful for researchers working in the field of robotics and for designers to develop new type of artificial muscle depending on the applications.