We discuss the use of algebraic multigrid methods in solving PDEs arising from the Maxwell equations for photonic crystal systems in the frequency domain. We begin by describing photonic crystals, their unique properties, and some of their applications. We then discuss the difficulties inherent in time-harmonic Maxwell systems. We demonstrate successful solution of two-dimensional systems, where the Maxwell equations reduce to a scalar indefinite Helmholtz equation. We then show a remarkable correspondence between the convergence behavior of the solver and the physical properties of the system. Finally, we discuss current work toward generalizing our approach to fully-vectorial Maxwell systems.