This paper presents a theoretical realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry. The authors show how to construct analogs of quantum Hall edge states in photonic crystals made with non-reciprocal (Faraday-effect) media, which form one-way waveguides that allow electromagnetic energy to flow in only one direction. These waveguides are analogous to the chiral edge states of electrons in the quantum Hall effect. The key ingredient is the presence of non-reciprocal media that break time-reversal symmetry. The paper discusses the concept of photonic Chern numbers, which are topological invariants similar to the electronic Chern number. If the total Chern number changes across an interface separating two photonic band gap (PBG) media, there will be states localized to the interface with a non-zero net current. These states form the "one-way waveguides." The authors demonstrate that such waveguides can be realized in a 2D periodic photonic metamaterial with a domain wall, where the direction of the Faraday axis reverses. The unidirectional edge states are guaranteed if the Faraday effect generates photonic bands with non-zero Chern numbers. They construct photonic bands with non-zero Chern numbers in a hexagonal array of dielectric rods with a Faraday effect. The paper also discusses the theoretical framework for the Maxwell normal-mode problem in loss-free linear media with spatially-periodic local frequency-dependent constitutive relations. The non-reciprocal parts of the local permittivity and permeability tensors are odd imaginary functions of frequency, leading to a generalized self-consistent Hermitian eigenproblem. The authors show that the Berry curvature satisfies a k-space analog of the Gauss law, with monopole singularities emitting total Berry flux. The integer Chern invariant associated with any compact surface in k-space is calculated, and it is shown that when time-reversal symmetry is broken, the Chern numbers of the bands become non-zero. The paper concludes that "one-way waveguides" can be constructed using non-reciprocal photonic crystals. The key idea is to start with a band structure that has both time-reversal and inversion symmetry, allowing the existence of Dirac points. When time-reversal symmetry is broken, the Chern numbers of the bands become non-zero, leading to unidirectional edge states. The authors also discuss the technical challenges of designing such structures and the importance of having a large Verdet coefficient in the material to achieve the Faraday effect.This paper presents a theoretical realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry. The authors show how to construct analogs of quantum Hall edge states in photonic crystals made with non-reciprocal (Faraday-effect) media, which form one-way waveguides that allow electromagnetic energy to flow in only one direction. These waveguides are analogous to the chiral edge states of electrons in the quantum Hall effect. The key ingredient is the presence of non-reciprocal media that break time-reversal symmetry. The paper discusses the concept of photonic Chern numbers, which are topological invariants similar to the electronic Chern number. If the total Chern number changes across an interface separating two photonic band gap (PBG) media, there will be states localized to the interface with a non-zero net current. These states form the "one-way waveguides." The authors demonstrate that such waveguides can be realized in a 2D periodic photonic metamaterial with a domain wall, where the direction of the Faraday axis reverses. The unidirectional edge states are guaranteed if the Faraday effect generates photonic bands with non-zero Chern numbers. They construct photonic bands with non-zero Chern numbers in a hexagonal array of dielectric rods with a Faraday effect. The paper also discusses the theoretical framework for the Maxwell normal-mode problem in loss-free linear media with spatially-periodic local frequency-dependent constitutive relations. The non-reciprocal parts of the local permittivity and permeability tensors are odd imaginary functions of frequency, leading to a generalized self-consistent Hermitian eigenproblem. The authors show that the Berry curvature satisfies a k-space analog of the Gauss law, with monopole singularities emitting total Berry flux. The integer Chern invariant associated with any compact surface in k-space is calculated, and it is shown that when time-reversal symmetry is broken, the Chern numbers of the bands become non-zero. The paper concludes that "one-way waveguides" can be constructed using non-reciprocal photonic crystals. The key idea is to start with a band structure that has both time-reversal and inversion symmetry, allowing the existence of Dirac points. When time-reversal symmetry is broken, the Chern numbers of the bands become non-zero, leading to unidirectional edge states. The authors also discuss the technical challenges of designing such structures and the importance of having a large Verdet coefficient in the material to achieve the Faraday effect.