Soft robots offer extraordinary advantages in terms of flexibility, shape morphology, human-robot compatibility, and functionality. These robots are often able to bend and deform to arbitrary shapes by using compliant and elastic materials, which allow them to perform complex motions or maneuvers. While there are many benefits to their design, these systems often lack the speed and power of conventional robots or rely on rigid actuators, motors, or pumps. This proposal describes a new approach to developing soft systems that maintain the benefits of conventional robots through the use of soft electromagnetic actuators. Specifically, this proposal aims to explore new designs for soft actuators using liquid metal conductors, compliant permanent magnets, and elastic polymers. This work presents new architectures for soft actuators, including bio-inspired linear systems and a rotary motor with novel magnetic field sensors. Each system is characterized to evaluate performance metrics such as speed and force/torque production, which are orders of magnitude higher than existing soft actuators. New applications for soft electromagnetic actuators are also demonstrated including fully soft pumps, hybrid-soft vehicles, and squeezable speed controllers. This article also proposes further work to extend applications beyond those achievable with conventional electromagnetic actuators through coil deformation and liquid metal strain sensing. The proposed work includes a new design and characterization of a soft electromagnetic actuator as well as applications for locomotion that showcase the advantages of deformable bodies. Long term, these actuators could be integrated into complex soft-body systems or wearable devices.