Enzyme catalysis enables complex biotransformation to be imitated. This biomimetic approach allows for the application of enzymes in a variety of catalytic processes. Nevertheless, enzymes need to be shielded by a support material under challenging catalytic conditions due to their intricate and delicate structures. Specifically, metal-organic frameworks and covalent-organic frameworks (MOFs and COFs) are increasingly popular for use as enzyme-carrier platforms because of their excellent tunability in structural design as well as remarkable surface modification. These porous organic framework capsules that host enzymes not only protect the enzymes against harsh catalytic conditions but also facilitate the selective diffusion of guest molecules through the carrier. This review summarizes recent progress in MOF-enzyme and COF-enzyme composites and highlights the pore structures tuned for enzyme encapsulation. Furthermore, the critical issues associated with interactions between enzymes and pore apertures on MOF- and COF-enzyme composites are emphasized, and perspectives regarding the development of high-quality MOF and COF capsules are presented.