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Graphene and graphene oxide (GO), as wonder materials, have penetrated nearly every field of research. One of their most attractive features is the functionality and assembly of graphene or GO, in which they can be considered to be chemically functionalized building blocks for creating unconventional porous graphene materials (PGMs) that not only combine the merits of both porous materials and graphene, but also have major advantages over other porous carbons for specific applications. The chemistry and approaches for functionalizing graphene and GO are first introduced, and typical procedures for pore creation (e.g., in-plane pores, 2D laminar pores, and 3D interconnected pore assemblies), self-assembly, and tailoring mechanisms for PGMs to highlight the significance of precise control over the pore morphology and pore size are summarized. Because of their unique pore structures, with different morphologies and intriguing properties, PGMs serve as key components in a variety of applications such as energy storage, electrocatalysis, and molecular separation. Finally, the challenges relating to PGMs from the understanding of chemical self-assembly to specific applications are discussed, and promising solutions on how to tackle them are presented. This provides an insightful outlook for the future development of the chemistry and applications of PGMs. [ABSTRACT FROM AUTHOR]