Photons, as the fundamental particles of light, possess unique properties that make them well-suited for information processing, communication, and data transfer. These advantages stem from their inherent characteristics, such as the zero rest mass that allows light-speed propagation, the neutral charge that blocks electromagnetic interference, and the limited interaction with matter, which minimizes Joule heating. Drawing inspiration from the intriguing properties of topological materials in condensed matter physics, the recently emerging photonic topological insulator is a groundbreaking innovation for realizing robust light transmission. In a photonic topological insulator, light waves are manipulated to flow along the surface of or the interface between materials while being immune to the backscattering caused by defects or imperfections. The implications of photonic topological insulators are profound for photonic information processing. They enable the creation of resilient, low-loss pathways, making them ideal for applications in photonic computing and quantum information processing. These materials can potentially revolutionize the development of photonic devices, leading to more efficient and reliable information processing systems. In this dissertation, I start by introducing the fundamental concepts in condensed matter physics that give rise to topological robustness, focusing on the quantum valley Hall effect and the quantum spin Hall effect. The photonic crystals supporting two analogous effects, the valley photonic crystal and the spin photonic crystal, are the cornerstones that pave the way for several designs and structures I proposed and analyzed throughout my Ph.D. These photonic designs, when I delve into the details, display some peculiar and previously overlooked properties, some of which hinder their applications in realistic scenarios. I present the following three designs, discuss their properties (including potential limitations), and provide first-principle-based analyses, which lead to solutions or improvements. The first demonstration is about a novel mechanism for optical energy localization that can be used to enhance light-matter interaction from a different perspective: redistributing the electromagnetic eigenmode inside a cavity to form an increased maximum value. This unique optical energy localization is due to the near-conservation of the valley degree of freedom, a binary index granted by the valley photonic crystals. When we use a mirror to terminate a waveguide that carries topologically robust modes associated with the valley index, the mode experiences a usual or delayed reflection at the mirror surface, depending on the geometry (orientation) of the mirror. The delayed reflection results in an optical energy localization at the mirror surface and enables the optimal eigenmode redistribution — When both ends of a topological waveguide are terminated with the designed mirrors, the resulting Fabry-Pérot cavity supports unusual eigenmodes with high values at the boundaries (mirror surfaces), where, if a quantum light emitter is placed, would significantly enhance the light-matter interaction due to the high electric field. Such an opportunity cannot be offered by a conventional Fabry-Pérot cavity because its eigenmodes show a standing-wave pattern with a set of local maxima. Next, I present two essential prerequisite tasks for robust photonic valley information processing: exciting a mode with a specific valley polarization and measuring the projection of a mode into the valley basis. To fully exploit the two-dimensional valley basis, we use a multimode topological waveguide made by interfacing two spin photonic crystals, whose eigenmodes are characterized by two binary indices, the (pseudo-) spin and the valley. The spin is associated with the propagation direction, and, along each direction, there are two modes with different valleys propagating at the same speed, which form the valley basis. The electromagnetic field distributions of the two co-propagating modes are different, enabling the selective valley-polarization excitation with a single linearly polarized dipole source. To identify the valley-polarization of a combination of the two co-propagating modes, we project them to the valley basis by physically separating them into two single-mode waveguides, each of which can only support one valley-polarization. By measuring the output energy of both single-mode waveguides, we characterize the combined mode with the valley basis. Then, I demonstrate a forward step of robust photonic valley information processing, manipulating the valley degree of freedom. This requires sufficient interaction between the two valleys, which does not exist in the multimode topological waveguide used in the valley-selective excitation because its eigenmode basis is the valley basis. The separation of the two valleys stems from the unique discrete translational symmetry of the waveguide. By rearranging the building blocks, the spin photonic crystals, to form a different interface, we build another waveguide where the two valleys are folded to overlap in the momentum space, enabling strong intervalley coupling. A valley-polarized mode propagating in such a waveguide undergoes a Rabi oscillation — its projection to the valley basis oscillates with respect to time and the strength of intervalley coupling. Although the propagation time can easily be tuned by varying the waveguide length, it is rarely deployed in practice because it requires a change of the structural size. I design and experimentally demonstrate that small geometric perturbations in the topological waveguide are sufficient to realize the desired tunable intervalley coupling. Finally, I discuss three phenomena that could potentially limit the engineering value of the designs, provide first-principle-based analyses, and offer possible solutions. (i) The robustness of the waveguide based on valley photonic crystals is not perfect and shows a unique dependence on the band gap width. This imposes a fundamental limit to the operating bandwidth of those waveguides; (ii) The finite-size effect affects the valley projection measurements and can be calibrated by modeling the evanescent tails; (iii) When a valley-polarized mode with low momentum (k→0) undergoes a Rabi oscillation in the multimode topological waveguide, it is not perfectly robust because the perturbation affects the spin basis. I extend the cavity perturbation theory to model photonic crystal waveguides, unfold how the four modes hybridize, and identify a frequency range where the robustness is only minimally compromised. This perturbation theory-based technique is applicable to all lossless periodic structures and can be used for carefully examining and improving the robustness of photonic topological insulators.