Covalent organic frameworks (COFs) are a class of crystalline porous polymers in which organic building blocks with specific geometries are connected through reversible covalent bond formation. The synthesis and development of COFs strongly rely on dynamic covalent chemistry. COFs feature rigid porous structures, high porosity, and high modularity. Their functionalities, topologies, as well as chemical and physical properties can be fine-tuned via organic synthesis. This review introduces the synthesis principles, linkage types, two- and three-dimensional structures, and processing of COFs. Furthermore, insights into the growing applications of COFs, including gas storage and separations, catalysis, energy storage and conversion, optoelectronics, sensing, and drug delivery are discussed.