The current status of graphene edge fabrication and characterization is reviewed in detail. We first compare different fabrication methods, including the chemical vapor deposition method, various ways of unzipping carbon nanotubes, and lithographic methods. We then summarize the different edge/ribbon structures that have been produced experimentally or predicted theoretically. We discuss different characterization tools, such as transmission electron microscopy and Raman spectroscopy, that are currently used for evaluating the edge quality as well as the atomic structures. Finally, a detailed discussion of defective and folded edges is also presented. Considering the short history of graphene edge research, the progress has been impressive, and many further advances in this field are anticipated.