Soft actuators are deformable materials that change their dimensions or shape in response to external stimuli. Among the various stimuli, remote magnetic fields are one of the most attractive forms of actuation, due to their ease of use, fast response, and safety in biological systems. Composites of magnetic particles with polymer matrices are the most common materials for magnetic soft actuators. In this paper, we demonstrate the fabrication and actuation of magnetic shape-memory materials based on hydrogels containing field-structured magnetic particles. These actuators are formed by placing the pregel dispersion into a mold of the desired on-field shape and exposing it to a homogeneous magnetic field until the gel point is reached. At this point, the material may be removed from the mold and fully gelled in the desired off-field shape. The resultant magnetic shape-memory material then transitions between these two shapes when it is subjected to successive cycles of a homogeneous magnetic field, acting as a large deformation actuator. For actuators that are planar in the off-field state, this can result in significant bending to return to the on-field state. In addition, it is possible to make shape-memory materials that twist under the application of a magnetic field. For these torsional actuators, both experimental and theoretical results are given.