Using ab-initio tight binding models and modern numerical methods, the spectral properties of aperiodic 2D materials with millions of atoms can be investigated. Recent calculations for the electronic density of states (DoS) in twisted bilayer systems of graphene and transition metal di-chalcogenides (TMDCs) will be presented. Some DoS features appear across many different materials, and possible explanations of their origin will be provided. Of particular importance is finding useful ways of viewing the electronic spectrum when conventional Bloch theory, and thus crystal momentum, is not applicable due to lack of symmetry.