The inherent limitations of graphene in the context of electronic applications due to the absence of a band-gap can be overcome by combining it with materials that are intrinsically semiconducting (like the family of transition metal dichalcogenides) or insulating (like hexagonal boron nitride). Combinations of such materials in layered heterostructures provide interesting opportunities to improve and manipulate their intrinsic properties due to the weak van der Waals interaction between layers, which preserves their basic character but allows for important variations. These layered heterostructures present also a challenge to theory, since they are typically incommensurate and cannot be readily described by the standard band theory. We will discuss recent progress in addressing these challenges, using perturbation theory approaches and tight-binding hamiltonians derived from ab-initio results by application of maximally localized Wannier orbitals. We will also present some ideas for applications of these layered heterostructures to electronic, optical and plasmonic devices.