In this chapter, we describe various approaches to computing the spectra of photonic quasicrystals (PQCs). We focus on a recently developed super-space method for computing the spectra and eigenstates of PQCs defined by the standard cut-and-project construction, that involves directly solving Maxwell s equations in higher dimensions, where a generalization of Bloch s theorem applies. We emphasize the conceptual and practical differences between super-space and supercell methods, which involve computing the eigenfrequencies and/or local density of states to an approximation of the true aperiodic structure.