Graphene has unique physical properties, and a variety of proof-of-concept devices based on graphene have been demonstated. A prerequisite for the application of graphene is its production in a controlled manner because the number of graphene layers and the defects in these layers significantly influence transport properties. In this paper, we briefly review our recent work on the controlled synthesis of graphene and graphene-based composites, the development of methods to characterize graphene layers, and the use of graphene in clean energy applications and for rapid DNA sequencing. For example, we have used Auger electron spectroscopy to characterize the number and structure of graphene layers, produced single-layer graphene over a whole Ni film substrate, synthesized well-dispersed reduced graphene oxide that was uniformly grafted with unique gold nanodots, and fabricated graphene nanoscrolls. We have also explored applications of graphene in organic solar cells and direct, ultrafast DNA sequencing. Finally, we address the challenges that graphene still face in its synthesis and clean energy and biological sensing applications.