Covalent organic frameworks (COFs) are a class of crystalline porous organic polymers assembled by connecting organic building units via covalent bonds. They are characterized as extended two-dimensional (2D) or three-dimensional (3D) frameworks with precise spatial structures and building block distribution. A key feature of COFs is their inherent porosity originating from their well-ordered nanopores which are designable, tunable and modifiable through pore engineering. This review describes the pore engineering of 2D COFs based on their framework topologies. It begins with a brief summary of the pore design principles of 2D COFs which are composed of uniform micropores or mesopores. Then the state-of-the-art progress achieved in a new branch of 2D COFs, that is, heteropore COFs, which possess multiple-pore skeletons and thus exhibit hierarchical porosity, is comprehensively reviewed, including their design strategies, synthesis, characterization, properties and applications. In the last part, personal perspectives on this emerging class of 2D polymers with complex structures and hierarchical porosity are discussed.