The celebrated electronic properties of graphene have opened way for materials just one-atom-thick to be used in the post-silicon electronic era. An important milestone was the creation of heterostructures based on graphene and other two-dimensional (2D) crystals, which can be assembled in 3D stacks with atomic layer precision. These layered structures have already led to a range of fascinating physical phenomena, and also have been used in demonstrating a prototype field effect tunnelling transistor - a candidate for post-CMOS technology. The range of possible materials which could be incorporated into such stacks is very large. Indeed, there are many other materials where layers are linked by weak van der Waals forces, which can be exfoliated and combined together to create novel highly-tailored heterostructures. Here we describe a new generation of field effect vertical tunnelling transistors where 2D tungsten disulphide serves as an atomically thin barrier between two layers of either mechanically exfoliated or CVD-grown graphene. Our devices have unprecedented current modulation exceeding one million at room temperature and can also operate on transparent and flexible substrates.