This article reviews the basic theoretical aspects of octagraphene,an one-atom-thick allotrope of carbon,with un-usual two-dimensional (2D) Fermi nesting,hoping to contribute to the new family of quantum materials.Octagraphene has an almost strongest sp2 hybrid bond similar to graphene,and has the similar electronic band structure as iron-based superconductors,which makes it possible to realize high-temperature superconductivity.We have compared various pos-sible mechanisms of superconductivity,including the unconventional s± superconductivity driven by spin fluctuation and conventional superconductivity based on electron-phonon coupling.Theoretical studies have shown that octagraphene has relatively high structural stability.Although many 2D carbon materials with C4 carbon ring and C8 carbon ring structures have been reported,it is still challenging to realize the octagraphene with pure square-octagon structure experimentally.This material holds hope to realize new 2D high-temperature superconductivity.