In this paper, we investigate the electrical behavior of transistors based on a vertical graphene-hexagonal boron nitride (hBN) heterostructure, using atomistic multiphysics simulations based on density-functional theory and non-equilibrium Green’s function formalism. We show that the hBN current-blocking layer is effective and allows modulation of the current by five orders of magnitude, confirming experimental results. We also highlight—through accurate numerical calculations and simpli- fied analytical modeling—some intrinsic limitations of vertical heterostructure transistors. We show that the overlap between gate contacts and source/drain leads screens the electric field induced by the gates and is responsible for the excessive degradation of the sub-threshold swing, the ION/IOFF ratio, and the cut-off frequency.