The paper discusses the analogs of quantum Hall effect (QHE) edge states in photonic crystals, specifically those built with time-reversal-symmetry-breaking Faraday-effect media. These photonic systems exhibit "chiral" edge modes that propagate unidirectionally along boundaries where the Faraday axis reverses. The authors argue that these modes are analogous to QHE edge states and are immune to backscattering and localization by disorder. The "Berry curvature" of the photonic bands plays a role similar to the magnetic field in the QHE, and explicit calculations demonstrate the existence of such unidirectionally-propagating photonic edge states. The introduction highlights the potential of photonic band-gap (PBG) materials and metamaterials in controlling light flow, emphasizing the importance of spatial and time-reversal symmetries in understanding the dynamics of wavepackets. The paper then delves into the formalism of the Maxwell normal mode problem in periodic, loss-free media, discussing the Berry curvature and its role in the photonic bandstructure problem. It explains how broken time-reversal symmetry can lead to the appearance of topological defects in the gauge field, such as phase singularities, which are analogous to the Chern number in the QHE. The authors propose a strategy for constructing photonic bands with non-zero Chern invariants and "chiral" edge states by using magneto-optic materials and hexagonal lattice geometry. They show that Dirac points, where the Chern numbers of bands can be exchanged, can be created at isolated points in the Brillouin zone. The paper concludes with numerical examples and semiclassical calculations confirming the existence of these edge states.The paper discusses the analogs of quantum Hall effect (QHE) edge states in photonic crystals, specifically those built with time-reversal-symmetry-breaking Faraday-effect media. These photonic systems exhibit "chiral" edge modes that propagate unidirectionally along boundaries where the Faraday axis reverses. The authors argue that these modes are analogous to QHE edge states and are immune to backscattering and localization by disorder. The "Berry curvature" of the photonic bands plays a role similar to the magnetic field in the QHE, and explicit calculations demonstrate the existence of such unidirectionally-propagating photonic edge states. The introduction highlights the potential of photonic band-gap (PBG) materials and metamaterials in controlling light flow, emphasizing the importance of spatial and time-reversal symmetries in understanding the dynamics of wavepackets. The paper then delves into the formalism of the Maxwell normal mode problem in periodic, loss-free media, discussing the Berry curvature and its role in the photonic bandstructure problem. It explains how broken time-reversal symmetry can lead to the appearance of topological defects in the gauge field, such as phase singularities, which are analogous to the Chern number in the QHE. The authors propose a strategy for constructing photonic bands with non-zero Chern invariants and "chiral" edge states by using magneto-optic materials and hexagonal lattice geometry. They show that Dirac points, where the Chern numbers of bands can be exchanged, can be created at isolated points in the Brillouin zone. The paper concludes with numerical examples and semiclassical calculations confirming the existence of these edge states.