Jamming is a popular and versatile soft robotic mechanism, enabling new systems to be developed that can achieve high stiffness variation with minimal volume variation. Numerous applications have been reported, including deep-sea sampling, industrial gripping, and use as paws for legged locomotion. This review explores the state-of-the-art for the three classes of jamming actuator: granular, layer and fibre jamming. We highlight the strengths and weaknesses of these soft robotic systems and propose opportunities for further development. We describe a number of trends, promising avenues for innovative research, and several technology gaps that could push the field forwards if addressed, including the lack of standardization for evaluating the performance of jamming systems. We conclude with perspectives for future studies in soft jamming robotics research, particularly elucidating how emerging technologies, including multi-material 3D printing, can enable the design and creation of increasingly diverse and high-performance soft robotic mechanisms for a myriad of new application areas.