Abstract: Covalent organic frameworks (COFs) are crystalline porous polymers constructed by the covalent linkage of building blocks in a predictable pattern. In 2005, Yaghi and co-workers addressed the topological design principles of COFs and synthesized the first example with hexagonal pore channels and layer-by-layer stacking structures. The advent and development of COFs over years have been providing a promising platform across scientific fields as well as opportunities of designing the state-of-art 2D architectures. Given the covalent linkages and organic components, both the chemical and thermal stability of COFs are improved significantly, and the mass density is much lower than the well-known metal-organic frameworks. Different from the amorphous porous organic materials, the long-range ordered structure of COFs can be pre-designed and tailored to realize the specific topological structures and pore properties. In recent years, extensive attention has been gained on COFs' chemistry including building units, topology structures, reaction types, polymerization methods and functional strategies. These studies have laid the foundation for the extension of COFs' applications such as gas storage/separation, catalysis, chemosensing, light harvesting, proton conduction and energy storage/transduction. Therefore, COFs not only exhibit the application value of porous organic materials, but also show great potential to challenge the bottlenecks of the emerging energy and environmental issues. In this review, we summarize the milestones in design and synthesis of COFs as well as the major progress achieved in applications, and further address their prospects and challenges in the future development.