This paper presents an analog of the quantum Hall effect (QHE) in photonic crystals. Photonic crystals with time-reversal-symmetry-breaking Faraday-effect media can exhibit "chiral" edge modes that propagate unidirectionally along boundaries where the Faraday axis reverses. These modes are analogous to the electronic edge states of QHE systems and are immune to backscattering and localization by disorder. The Berry curvature of the photonic bands plays a role similar to that of the magnetic field in QHE. The paper discusses the formalism of the Maxwell normal-mode problem in periodic, loss-free media, the Berry curvature of the photonic bandstructure, and the effects of broken time-reversal symmetry. It provides explicit numerical examples of bandstructures with non-trivial topological properties and shows the occurrence of edge states along domain wall configurations. A simple Dirac Hamiltonian is derived from the Maxwell equations using symmetry arguments, and it is shown that under certain conditions, the zero modes of this Hamiltonian exhibit anomalous currents along a single direction due to the breaking of time-reversal symmetry. The paper also discusses the topological structure of the photon bands, the Chern invariant, and the connection between edge modes and Chern invariants. It concludes with a discussion of the implications of these findings for photonic systems.This paper presents an analog of the quantum Hall effect (QHE) in photonic crystals. Photonic crystals with time-reversal-symmetry-breaking Faraday-effect media can exhibit "chiral" edge modes that propagate unidirectionally along boundaries where the Faraday axis reverses. These modes are analogous to the electronic edge states of QHE systems and are immune to backscattering and localization by disorder. The Berry curvature of the photonic bands plays a role similar to that of the magnetic field in QHE. The paper discusses the formalism of the Maxwell normal-mode problem in periodic, loss-free media, the Berry curvature of the photonic bandstructure, and the effects of broken time-reversal symmetry. It provides explicit numerical examples of bandstructures with non-trivial topological properties and shows the occurrence of edge states along domain wall configurations. A simple Dirac Hamiltonian is derived from the Maxwell equations using symmetry arguments, and it is shown that under certain conditions, the zero modes of this Hamiltonian exhibit anomalous currents along a single direction due to the breaking of time-reversal symmetry. The paper also discusses the topological structure of the photon bands, the Chern invariant, and the connection between edge modes and Chern invariants. It concludes with a discussion of the implications of these findings for photonic systems.