Continued rapid advances in materials science are closing the gap between the performance of polymer artificial muscles and natural skeletal muscle. Already, dielectric elastomers and polymer coil muscles can exceed the high strokes and fast response of natural muscle. The power densities of these artificial muscles are much greater than natural muscle and even exceed that of similarly sized conventional motors and engines. For example, polymer coil muscles have a power-to-weight ratio equivalent to a jet engine and 5 times higher than a car's petrol engine. These materials are cheap, strong, and easily fabricated from readily-available polymer fibres used for fishing lines and sewing threads. These and other polymer artificial muscles are inspiring new applications, especially where mechanical force and movement are needed and space is limited. Bio-inspired robotic applications include prosthetic hands, crawling worm-like robots, and swimming robot fish. This chapter summarises the different types of polymer artificial muscles, including performance comparisons, details on the operating mechanisms, and examples of bio-inspired robotic applications.