Magnetic shape memory alloys (MSMAs), both in condensed matter physics and in material science, are one of the most extensive research subjects. They show prompt response to the external magnetic field and give rise to large strain and have fine reversibility. The well-known example is Heusler-type MSMAs, which possess excellent multifunctional properties and have potential applications in energy transducer, actuator, sensor, microelectromechanical system, and magnetic refrigerator. In this paper, it is shown the recent progress in magnetostructural transformation, magnetic properties, shape deformation, magnetocaloric effect as well as magnetic field-induced shape memory effect in Ni-Mn-Ga, NiMnZ (Z = In, Sn, Sb), and NiCoMnZ (Z = In, Sn, Sb, Al) Heusler-type MSMAs. The remaining issues and possible challenges are briefly discussed.