Research on two-dimensional (2D) materials currently occupies a sizeable fraction of the materials science community, which has led to the development of a comprehensive body of knowledge on such layered structures. However, the goal of this thesis is to deepen the understanding of the comparatively unknown heterostructures composed of different stacked layers. First, we utilise linear-scaling density functional theory (LS-DFT) to simulate intricate interfaces between the most promising layered materials, such as transition metal dichalcogenides (TMDC) or black phosphorus (BP) and hexagonal boron nitride (hBN). We show that hBN can protect BP from external influences, while also preventing the band-gap reduction in BP stacks, and enabling the use of BP heterostructures as tunnelling field effect transistors. Moreover, our simulations of the electronic structure of TMDC interfaces have reproduced photoemission spectroscopy observations, and have also provided an explanation for the coexistence of commensurate and incommensurate phases within the same crystal. Secondly, we have developed new functionality to be used in the future study of 2D heterostructures, in the form of a linear-response phonon formalism for LS-DFT. As part of its implementation, we have solved multiple implementation and theoretical issues through the use of novel algorithms.