Originating from the studies of two-dimensional condensed-matter states, the concept of a topological order has recently been expanded to other fields of physics and engineering, particularly optics and photonics. Topological photonic structures have already overturned some of the traditional views on wave propagation and manipulation. The application of topological concepts to guided wave propagation has enabled novel photonic devices, such as reflection-free sharply bent waveguides, robust delay lines, spin-polarized switches and non-reciprocal devices. Discrete degrees of freedom, widely used in condensed-matter physics, such as spin and valley, is now entering the realm of photonics. In this talk, I will summarize the latest advances in this highly dynamic field, with special emphasis on our recent works related to two- and three-dimensional all-dielectric topological structures, as well as spin and valley, polarized one-way Klein tunneling in topologically nontrivial systems.