The paper discusses recent progress in the field of solitons in photonic topological insulators and describes the results of recent experiments with nonlinear topological states in static, invariable in the direction of light propagation,and dynamically modulated (mainly periodically) in the direction of light propagation Su—Schrieffer—Heeger waveguide arrays fabricated using the femtosecond laser writing technique. Such objects represent one of the simplest models of a topologically nontrivial structure. Solitons in topological insulators bifurcate with increase of power of laser beam from linear edge states in the topological bandgap of the system, inheriting topological protection of such states. Spatial localization of the soliton and the position of its propagation constant in the topological bandgap depend on its power and can be effectively and all-optically controlled. The paper discusses experimental observation of switching of the edge states from topological bandgap between twoclosely spaced dimerized Su—Schrieffer—Heeger arrays, the rate of which depends on the radiation intensity. Such switching can be completely arrested at sufficiently high powers. In trimer waveguide arrays, whose spectrum features two topological bandgaps with edge states of different symmetries simultaneously appearing in them, we observed two coexisting types of topological solitons with different stability properties. We alsodiscuss first experimental observation of π-solitons — nonlinear topological Floquet states that periodically reproduce their profiles in one-and two- dimensional Su—Schrieffer—Heeger waveguide arrays modulated in the direction of light propagation.