This review highlights various design and synthesis approaches toward the construction of ZMOFs, that is MOFs with topologies and, in some cases, features akin to traditional inorganic zeolites. The interest in this unique subset of MOFs is correlated with their exceptional characteristics arising from the periodic pore systems and distinctive cage-like cavities, in conjunction with modular intra- and/or extra-framework components, which ultimately allow for tailoring of pore size, pore shape, and/or properties towards specific applications.