This review offers an overview of the latest developments in metal-covalent organic framework (MCOF) and covalent metal-organic framework (CMOF) materials, whose construction entails a combination of reversible coordination and covalent bonding adapted from metal-organic frameworks (MOFs) and covalent organic frameworks (COFs), respectively. With an emphasis on the MCOF and CMOF structures, this review surveys their building blocks and topologies. Specifically, the frameworks are classified based on the dimensions of their components (building blocks), namely, discrete building blocks and one-dimensional infinite building blocks. For the first category, the materials are further divided into collections of two- and three-dimensional networks based on their topologies. For the second category, the recently emerging MCOFs with woven structures are covered. Finally, the state-of-the-art in MCOF and CMOF chemistry has been laid out for promising avenues in future developments.