Monolayer graphene exhibits extraordinary properties owing to the unique, regular arrangement of atoms in it. However, graphene is usually modified for specific applications, which introduces disorder. This article presents details of graphene structure, including sp 2 hybridization, critical parameters of the unit cell, formation of σ and π bonds, electronic band structure, edge orientations, and the number and stacking order of graphene layers. We also discuss topics related to the creation and configuration of disorders in graphene, such as corrugations, topological defects, vacancies, adatoms and sp 3 -defects. The effects of these disorders on the electrical, thermal, chemical and mechanical properties of graphene are analyzed subsequently. Finally, we review previous work on the modulation of structural defects in graphene for specific applications.