Magnetically responsive soft materials are soft composites where magnetic fillers are embedded into soft polymeric matrices. These active materials have attracted extensive research and industrial interest due to their ability to realize fast and programmable shape changes through remote and untethered control under the application of magnetic fields. They would have many high-impact potential applications in soft robotics/devices, metamaterials, and biomedical devices. With a broad range of functional magnetic fillers, polymeric matrices, and advanced fabrication techniques, the material properties can be programmed for integrated functions, including programmable shape morphing, dynamic shape deformation-based locomotion, object manipulation and assembly, remote heat generation, as well as reconfigurable electronics. In this review, an overview of state-of-the-art developments and future perspectives in the multifunctional magnetically responsive soft materials is presented.