Reduction in the dimensions of silicon based devices has produced extraordinary developments in the performance of electronic systems. Recently, the advantages and challenges that caused by silicon devices shrinking have been investigated in many studies. Most of them have concluded that silicon technology is coming to an end and new innovations are required in the near future. Graphene is the promising candidate material as building blocks for nanoelectronic industry in order to silicon technology replacement. Graphene is first two dimensional materials that has significant potential in future nanoelectronic devices and other nanotechnology applications; therefore, it is an attractive subject for the researchers and scientists. Graphene is a carbon allotrope and is the basic element of other carbon allotropes. In this paper, main graphene production approaches are mentioned. The mechanical, thermal, optical, electrical, electronic and other fundamental properties of graphene are introduced. Moreover, it is considered as a novel material with numerous applications, which, we mention a few of important utilizations of graphene and its derivatives. Then, the different types of defects in graphene and their specifications, the methods of defect generation, defect healing, and properties of defective graphene are studied. Graphene nanoribbons and their geometric structures, fabrication approaches and electronic specifications are investigated. The effects of width, vacancy defect and doping concentration on the band structure of the graphene nanoribbons are extracted with ATK software in this paper. Simulation results showed that by increasing in the width, vacancy defect and doping concentration of nanoribbons, their band gap were decreased. These properties are suitable for controlling the channel of graphene nanoribbon field effect transistors.