The remarkable quantum Hall effect, in which the motion of electrons confined to two dimensions is impervious to the effects of disorder as a result of topological protection, continues to inspire new and perhaps unexpected physics (there are many examples in our department alone).  In this colloquium I will present some of my group's recent work on the topological physics of photons - as opposed to electrons - with an emphasis on the interplay between topological protection and mean-field interactions and nonlinearity.  Specifically, I will describe our experimental demonstration of chiral edge state solitons, as well as the integer and fractionally quantized motion of solitons in Thouless pumps.