Soft robots are being developed to mimic the movement of biological organisms and as wearable garments to assist human movement in rehabilitation, training, and tasks encountered in functional daily living. Stretchable artificial muscles are well suited as the active mechanical element in soft wearable robotics, and here the performance of highly stretchable and compliant polymer coil muscles are described and analyzed. The force and displacements generated by a given stimulus are shown to be determined by the external loading conditions and the main material properties of free stroke and stiffness. Spring mechanics and a model based on a single helix are used to evaluate both the coil stiffness and the mechanism of coil actuation. The latter is directly coupled to a torsional actuation in the twisted fiber that forms the coil. The single helix model illustrates how fiber volume changes generate a partial fiber untwist, and spring mechanics shows how this fiber untwist generates large tensile strokes and high gravimetric work outputs in the polymer coil muscles. These analyses highlight possible as yet unexplored means for further enhancing the performance of these systems.