Covalent organic frameworks (COFs), connecting different organic units into one system through covalent bonds, are crystalline organic porous materials with 2D or 3D networks. Compared with conventional porous materials such as inorganic zeolite, active carbon, and metal-organic frameworks, COFs are a new type of porous materials with well-designed pore structure, high surface area, outstanding stability, and easy functionalization at the molecular level, which have attracted extensive attention in various fields, such as energy storage, gas separation, sensing, photoluminescence, proton conduction, magnetic properties, drug delivery, and heterogeneous catalysis. Herein, the recent advances in metal-free COFs as a versatile platform for heterogeneous catalysis in a wide range of chemical reactions are presented and the synthetic strategy and promising catalytic applications of COF-based catalysts (including photocatalysis) are summarized. According to the types of catalytic reactions, this review is divided into the following five parts for discussion: achiral organic catalysis, chiral organic conversion, photocatalytic organic reactions, photocatalytic energy conversion (including water splitting and the reduction of carbon dioxide), and photocatalytic pollutant degradation. Furthermore, the remaining challenges and prospects of COFs as heterogeneous catalysts are also presented.