The celebrated electronic properties of graphene(1,2) have opened the way for materials just one atom thick(3) to be used in the post-silicon electronic era(4). An important milestone was the creation of heterostructures based on graphene and other two-dimensional crystals, which can be assembled into three-dimensional stacks with atomic layer precision(5-7). Such layered structures have already demonstrated a range of fascinating physical phenomena(8-71), and have also been used in demonstrating a prototype field-effect tunnelling transistor(12), which is regarded to be a candidate for post-CMOS (complementary metal-oxide semiconductor) technology. The range of possible materials that could be incorporated into such stacks is very large. Indeed, there are many other materials with layers linked by weak van der Waals forces that can be exfoliated(3,13) and combined together to create novel highly tailored heterostructures. Here, we describe a new generation of field-effect vertical tunnelling transistors where two-dimensional tungsten disulphide serves as an atomically thin barrier between two layers of either mechanically exfoliated or chemical vapour deposition-grown graphene. The combination of tunnelling (under the barrier) and thermionic (over the barrier) transport allows for unprecedented current modulation exceeding 1 x 10(6) at room temperature and very high ON current. These devices can also operate on transparent and flexible substrates.