As a result of the recent progress in fabricating large-area graphene sheets, graphene-based mechanical devices have become vastly easier to manufacture and now show even greater promise for a range of applications. This article reviews the progress of resonant graphene nanoelectromechanical systems and the possible applications of this technology to signal processing, sensing, and other areas. After discussing recent advances in fabrication and measurement techniques that make graphene resonators a viable technology, the article presents what is known about the performance of graphene mechanical systems. The authors also highlight unresolved questions, such as the source of the dissipation in graphene resonators, and discuss the progress made on these issues to date. The authors conclude with a discussion of important future directions for graphene research and the applications for which graphene nanomechanical devices may be well suited.