Fast, cheap, and reliable DNA sequencing could be one of the most disruptive innovations of this decade, as it will pave the way for personalized medicine. In pursuit of such technology, a variety of nanotechnology-based approaches have been explored and established, including sequencing with nanopores. Owing to its unique structure and properties, graphene provides interesting opportunities for the development of a new sequencing technology. In recent years, a wide range of creative ideas for graphene sequencers have been theoretically proposed and the first experimental demonstrations have begun to appear. Here, we review the different approaches to using graphene nanodevices for DNA sequencing, which involve DNA passing through graphene nanopores, nanogaps, and nanoribbons, and the physisorption of DNA on graphene nanostructures. We discuss the advantages and problems of each of these key techniques, and provide a perspective on the use of graphene in future DNA sequencing technology.