The dream to prepare well-defined materials drives the methodological evolution for molecular synthesis, structural control and materials manufacturing. Among various methods, chemical approaches to design, synthesize, control and engineer small molecules, polymers and networks offer the fundamental strategies. Merging covalent bonds and non-covalent interactions into one method to establish a complex structural composition for specific functions, mimicking biological systems such as DNA, RNA and proteins, is at the centre of chemistry and materials science. Covalent organic frameworks (COFs) are a class of crystalline porous polymers that enable the integration of organic units into highly ordered structures via polymerization. This polymerization system is unique as it deploys covalent bonds to construct the primary order structures of polymeric backbones via polycondensation and leverages on non-covalent interactions to create the high order structures of polymeric networks via supramolecular polymerization in a one-pot reaction system. This Primer covers all aspects of the field of COFs from chemistry to physics, materials and applications, and outlines the design principle, experimental methods, characterization and applications, with an aim to show a concise yet full picture of the field. The key fundamental issues to be addressed are analysed with an outlook on the future major directions from different perspectives.