Display omitted •A focus on the recent developments of supramolecular catalysis based on HCCs.•Metalloligand and self-sorting approaches are commonly used to construct HCCs.•Instances of catalytic macrocyclic or cage-like HCCs are discussed in detail. The rational design and facile construction of discrete heterometallic supramolecular catalysts have precipitated a surge of research interest in emulating sophisticated natural catalysts with well-defined cavities and inlaid active sites, allowing conversion of encapsulated substrates with high chemo-, regio-, and stereoselectivity. This review briefly highlights such discrete, heterometallic, coordination-driven metallacycles and metallacages obtained by the strategic utilization of a range of predesigned building blocks in the supramolecular chemist’s toolkit. The two major synthetic strategies toward these metalla-architectures are presented, and special attention has been paid to discussing both the fascinating structures and the unique catalytic performance of various heterometallic macrocycles and cages.