Soft robotics is a growing area of research which utilizes the compliance and adaptability of soft structures to develop highly adaptive robotics for soft interactions. One area in which soft robotics has the ability to make significant impact is in the development of soft grippers and manipulators. With an increased requirement for automation, robotics systems are required to perform task in unstructured and not well defined environments; conditions which conventional rigid robotics are not best suited. This requires a paradigm shift in the methods and materials used to develop robots such that they can adapt to and work safely in human environments. One solution to this is soft robotics, which enables soft interactions with the surroundings while maintaining the ability to apply significant force. This review paper assesses the current materials and methods, actuation methods and sensors which are used in the development of soft manipulators. The achievements and shortcomings of recent technology in these key areas are evaluated, and this paper concludes with a discussion on the potential impacts of soft manipulators on industry and society.