Metal-organic polyhedra are three dimensional discrete structures typically constructed by the self-assembly of metal ions and ligands. The synthesis and geometry of discrete structures entirely rely on the choice of metal ions, ligand constraints such as steric bulk, bend angle, and functionalities, and the nature of applied solvents. As a result, they provide tailorable internal volume and usually hydrophobic nature to the cavity that in turn makes them one of the prominent host molecules for a range of applications. This review highlights the intervention of ligand constraints, precisely bend angle (08, 608, 1208, and 1808), hydroxyl functionalities, and the role of concepts such as molecular panelling and subcomponent self-assembly in the synthesis of polyhedra.