Covalent organic frameworks (COFs) have been touted as a new class of porous crystalline materials for gas storage applications due to their high inherent surface areas, very low densities, high stability from the formation of covalent bonds, and tunable pore dimensions, ranging from ultramicropores to mesopores. Hydrogen storage of COFs at ambient pressure and temperature is low and far from meeting the Department of Energy requirements. Adsorption simulations of COFs show that doping with charged species can affect their capacity. In addition, membrane fabrication uses mild or harsh solvents and mechanical treatments; thus, the chemical and mechanical stability of COFs is another selection criterion. Other properties, like hydrophilicity/hydrophobicity, surface charge, and proton conductivity, also have a significant influence on the performance of COF-based membranes in various separations. A rational design strategy bridging the gap between COFs and COF-based membranes is the key to optimizing the advantages of COFs for precise and rapid membrane separation.