Different proposals of graphene transistors based on off-plane (i.e., vertical) transport, have recently appeared in the literature, exhibiting experimental current modulation of a factor 10(4)-10(5) at room temperature. These devices overcome the lack of bandgap that undermines the operation of graphene transistors, and positively exploit graphene's ultimate thinness, high conductivity, and low density of states. However, very little is known about vertical transport through graphene and two-dimensional materials, either in terms of experiments or theory. In this paper we will discuss the physics and the electronics of off-plane transport through heterostructures of graphene and 2D materials. We investigate transport across vertical heterostructures of 2D materials with multi-scale simulations, including first-principle density functional theory and non-equilibrium Green's functions based on NanoTCAD ViDES. We show that unexpected behaviors emerge, which are not observed in the more familiar semiconductor heterostructures based on III-V and II-VI materials systems, and that are not predicted by simplistic physical models. Such properties have a significant impact on the design and performance of transistors for digital or high frequency operations. (C) 2015 Elsevier Ltd. All rights reserved.