The CoCrFeMnNi alloy is one of the most notable first-generation high-entropy alloys and is also known as a Cantor alloy. This alloy was first proposed in 2004 and shows promising performance at cryogenic temperatures (CTs). Subsequent research has indicated that the equiatomic ternary CoCrNi medium-entropy alloy (MEA), as a subset of the Cantor alloy family, has better mechanical properties than the CoCrFeMnNi alloy. Interestingly, both the strength and ductility of the CoCrNi MEA are higher at CTs than at room temperature. CoCrNi-based alloys have attracted considerable attention in the metallic materials community and it is therefore important to generalize and summarize the latest progress in CoCrNi-based MEA research. The present review initially briefly introduces the discovery of the CoCrNi MEA. Subsequently, its tensile response and deformation mechanisms are summarized. In particular, the effects of parameters, such as critical resolved shear stress, stacking fault energy and short-range ordering, on the deformation behavior are discussed in detail. The methods for strengthening the CoCrNi MEA are then reviewed and divided into two categories, namely, modifying microstructures and adjusting chemical compositions. In addition, the mechanical performance of CoCrNi-based MEAs, including their dynamic shear properties, creep behavior and fracture toughness, is also deliberated. Finally, the development prospects of CoCrNi-based MEAs are proposed.