Graphene and other two dimensional (2D) materials are currently integrated into nanoscaled devices that may - one day - sequence genomes. The challenge to solve is conceptually straightforward: cut a sheet out of a 2D material and use the edge of the sheet to scan an unfolded biomolecule from head to tail. As the scan proceeds - and because 2D materials are atomically thin - the information provided by the edge might be used to identify different segments - ideally single nucleotides - in the biomolecular strand. So far, the most efficient approach was to drill a nano-sized pore in the sheet and use this pore as a channel to guide and detect individual molecules by measuring the electrochemical ionic current. Nanoscaled gaps between two electrodes in 2D materials recently emerged as powerful alternatives to nanopores. This article reviews the current status and prospects of integrating 2D materials in nanopores, nanogaps and similar devices for single molecule biosensing applications. We discuss the pros and cons, the challenges, and the latest achievements in the field. To achieve high-throughput sequencing with 2D materials, interdisciplinary research is essential.