This dissertation is a collection of four independent works whose common denominator is topological photonics. Some of these works describe the discoveryof new topological phases, some describe first principles implementation of theoretically predicted topological phases and some serve as bringing well-known topological phases to new material platforms or settings that have not been explored yet. In the first chapter I implement a theoretically predicted, yet often disregarded, topological phase predicted in graphe and bilayer graphene called the spin-valley topological insulator phase. The implementation is done on a microwave metawaveguide platform that has been used for the discovery of other photonic topological phases. I also explore high transmission and group velocity control applications using the spin-valley topological insulator phase. In the second chapter I discuss a novel second order topological phase called spin higher order topological insulator. This phase is somewhat analogous to the quantum spin Hall phase of electronic topological insulators in the sense that it introduces coupling between two different spins or pseudo-spins while maintaining topological robustness. In the third chapter I design a several first order topological insulators utilizing a plasma photonic crystal. These topological insulators utilize a plasma medium and a periodic metalic structure to impart a photonic crystal behavior on the plasma medium, thereby granting it topological properties. Additionally, I present the design of a second order topological insulator based on a plasma photonic crystal. I use the unique anistropic and frequency dependent permittivity of plasma to engineer a two-dimensional photonic crystal exhibiting topologically robust corner states. In the fourth and final chapter I describe an experimentally realizable implementation of the Su-Schrieffer-Heeger model of a one-dimensional topological insulator using surface plasmon polaritons. Due to the high loss nature of the typical surface plasmon polaritons, several engineering steps must be taken to allow for the signature of topological robust edge modes to be detectable.