In the last years, covalent organic frameworks, COFs, and their derived sub-groups based on auto-assembly of exclusively aromatic units, PAFs, are emerging into the advanced materials field due to their high free porous volume, structural regularity, robustness, hydrothermal stability, and functional variety. Their high gas uptake capacities, presence of stabilized active functions in the framework and charged low-density structures combined with their organization through π-conjugated system arrays open the possibilities of COFs and PAFs to be used as effective materials for adsorption, selective separation and catalysis, and in nanotechnological applications. This review will be focused on self-assembly synthesis mechanisms, physico-chemical characteristics, and applications of this class of promising covalent porous organic structures, outlooking their possible future approaches and perspectives.