A new approach has been developed to design organic polymers using topology diagrams. This strategy enables covalent integration of organic units into ordered topologies and creates a new polymer form, that is, covalent organic frameworks. This is a breakthrough in chemistry because it sets a molecular platform for synthesizing polymers with predesignable primary and high‐order structures, which has been a central aim for over a century but unattainable with traditional design principles. This new field has its own features that are distinct from conventional polymers. This Review summarizes the fundamentals as well as major progress by focusing on the chemistry used to design structures, including the principles, synthetic strategies, and control methods. We scrutinize built‐in functions that are specific to the structures by revealing various interplays and mechanisms involved in the expression of function. We propose major fundamental issues to be addressed in chemistry as well as future directions from physics, materials, and application perspectives. Up to the imagination: This Review shows the fundamentals for transforming covalent organic frameworks into designer structures in terms of both the skeletons and pores. The focus lies on functions based on interplays between photons, excitons, electrons, holes, ions, spins, and molecules, with structure–function correlations and framework‐specific properties described.