Topological photonics offers unique functionalities in light manipulation at the nanoscale by means of the so-called topological states which are robust against various forms of disorder. One of the simplest one-dimensional models supporting topological states is the Su-Schrieffer-Heeger model. In this paper, we review the physics of the Su-Schrieffer-Heeger model and its nonlinear counterparts exhibiting self-induced, tunable and many-particle edge states. We discuss the robustness of these states, highlighting their rich potential for nanophotonic and quantum optics applications.