Current refrigeration technologies based on compression cycles of greenhouse gases are environmentally threatening and cannot be scaled down to on-chip dimensions. Solid-state cooling is an environmentally friendly and highly scalable technology that may solve most of the problems associated with current refrigerant methods. Solid-state cooling consists of applying external fields (magnetic, electric, and mechanical) on caloric materials, which react thermally as a result of induced phase transformations. From an energy efficiency point of view, mechanocaloric compounds, in which the phase transitions of interest are driven by mechanical stresses, probably represent the most encouraging type of caloric materials. Conventional mechanocaloric materials like shape-memory alloys already display good cooling performances; however, in most cases they also present critical mechanical fatigue and hysteresis problems that limit their applicability. Finding new mechanocaloric materials and mechanisms that are able to overcome those problems, while simultaneously rendering large temperature shifts, is necessary to further advance the field of solid-state cooling. In this article, we review novel families of mechanocaloric materials that in recent years have been shown to be especially promising in the aspects that conventional mechanocaloric materials are not, and that exhibit unconventional but significant caloric effects. We emphasize elastocaloric materials, in which the targeted cooling spans are obtained through uniaxial stresses, since from an applied perspective they appear to be the most accomplished ones. Two different types of mechanocaloric materials emerge as particularly hopeful from our analysis: (1) compounds that exhibit field-induced order-disorder phase transitions involving either ions or molecules (polymers, fast-ion conductors, and plastic crystals), and (2) multiferroics in which the structural parameters are strongly coupled with the polar and/or magnetic degrees of freedom (magnetic alloys and oxide perovskites).