The last decade has witnessed the discovery of, and dramatic progress in understanding the physics of graphene and related two-dimensional materials. The development of methods for manufacturing and aligning high-quality two-dimensional crystals has facilitated the creation of a new generation of materials: the heterostructures of graphene with hexagonal crystals, in which the graphene electrons acquire new, qualitatively different properties. This thesis provides a comprehensive theoretical framework in which to understand these heterostructures, based on the tight binding model,...