In the quantum Hall effect, electrons confined to two dimensions and immersed in a perpendicular magnetic field are transported in a way that is entirely impervious to scattering by defects and disorder.  As a direct result, the Hall conductance is fixed to a fundamental constant of nature and can be measured to a precision of a part in ten billion, which has led to the redefinition of the kilogram.  In this talk I will demonstrate how this robustness of transport, called “topological protection,” is not limited to electrons, but rather is a general wave phenomenon that can also be applied to light propagating in artificial dielectric structures.  I will present my group’s recent experimental results on the nonlinear properties of photonic topological protection in waveguide arrays, including the observation of bulk and edge solitons and quantized soliton motion in photonic Thouless pumps.  Finally, I will describe our proposal for how photonic topological protection can be used to simultaneously overcome the fundamental obstacles of large backscattering and small bandwidth in slow-light systems.