Soft robotics as a field of study incorporates different mechanisms, control schemes, as well as multifunctional materials to realize robots able to perform tasks inaccessible to traditional rigid robots. Conventional methods for controlling soft robots include pneumatic or hydraulic pressure sources, and some more recent methods involve temperature and voltage control to enact shape change. Magnetism was more recently introduced as a building block for soft robotic design and control, with recent publications incorporating magnetorheological fluids and magnetic particles in elastomers, to realize some of the same objectives present in more traditional soft robotics research. This review attempts to organize and emphasize the existing work with magnetism and soft robotics, specifically studies on magnetic elastomers, while highlighting potential avenues for further research enabled by these advances.