Graphene edges determine the optical, magnetic, electrical, and electronic properties of graphene. In particular, termination, chemical functionalization and reconstruction of graphene edges leads to crucial changes in the properties of graphene, so control of the edges is critical to the development of applications in electronics, spintronics and optoelectronics. Up to date, significant advances in studying graphene edges have directed various smart ways of controlling the edge morphology. Though, it still remains as a major challenge since even minor deviations from the ideal shape of the edges significantly deteriorate the material properties. In this review, we discuss the fundamental edge configurations together with the role of various types of edge defects and their effects on graphene properties. Indeed, we highlight major demanding challenges to find the most suitable technique to characterize graphene edges for numerous device applications such as transistors, sensors, actuators, solar cells, light-emitting displays, and batteries in graphene technology.