Caloric properties rely on the reversible thermal response of a given material to changes induced by an applied field. In magnetic shape-memory materials, thanks to a strong interplay between magnetism and structure, caloric effects can be induced by application of both magnetic and mechanical (stress) fields. The study of such effects is an expanding field of research opening novel opportunities in solid state refrigeration and energy harvesting applications. In this paper we present an overview of the present state of the art of the subject. After a brief discussion of the thermodynamics of systems with magneto-structural interplay, we survey the caloric and multicaloric properties of NiMn-based Heusler materials. The conditions required for optimal caloric efficiency in cycling processes are considered. Finally, we outline some present challenges and future perspectives in this topic.