Next generation sequencing for DNA and proteins directly read the sequence of biopolymers from head-to-tail. Nanopores and nanogaps in two-dimensional materials, particularly graphene, are atomically thin edged-nanostructures that are prospected to scan biomolecules with atomic resolution. This chapter discusses the state of the art in fabrication methods for nano-sequencing devices, such as electron beam sculpting, di-electric breakdown and the use of intrinsically porous 2D membranes. In an operational nanopore device, a transmembrane potential is applied in the presence of an electrolyte and the ionic current flowing through the pore is measured. The translocation of a biopolymer results in a characteristic current blockade where the magnitude of the blockade can be linked to the molecular size of the translocating species. In nanogaps, on the other hand, it is the tunneling current between two opposing conductive graphene sheets which is measured. This chapter discusses the advantages and drawbacks of nanopores-nanogaps and strategies for future development.