In the quantum Hall effect, electron transport is highly robust - it is not hindered by the presence of defects and disorder.  This can be explained by a mapping of the Hall conductance to an abstract topological invariant, the Chern number.  This robustness is not limited to electrons in solid-state materials: it is a general wave phenomenon that can also apply to photons propagating in fabricated photonic crystal structures.  I will present our recent work in the field of topological photonics, including the observation of a topological transition, a bulk soliton residing in a topological band gap, and a proposal for how chiral edge states can overcome a key trade-off in slow-light devices.