Floquet topological physics, an area exploring periodically driven systems and leveraging degrees of freedom in the temporal dimension, has opened new avenues in photonics by enabling the creation of novel topological phases, new control mechanisms, and intriguing phenomena that are inaccessible or challenging to realize in static systems. These include anomalous Floquet topological insulators, anomalous Floquet Anderson insulators, and topological phases with broken time-reversal symmetry without the need for magnetic fields. Unlike conventional topological photonics, which relies on fixed structural or material properties to induce topological states, Floquet topological photonics leverages time-periodic modulation to access a broader range of topological effects, introducing flexibility in tuning topological transitions and wave dynamics. This review aims to provide a comprehensive overview of Floquet topological phases in photonic systems, explaining the theoretical basics, highlighting experimental platforms, the interplay with disorder, as well as the latest advancements beyond linear, Hermitian, Euclidean-geometry photonic systems, and recent progress in applications.