Understanding the intricacies of the interaction of light and matter is crucial to our perception of the world around us and for creating devices that harness light for technological applications. Many conventional devices such as telescopes, microscopes, cameras, and even reading glasses were based on early insights into the principles of refraction and reflection of light, whereas modern devices such as flat lenses, nano-antennas, and photonic waveguides are based on more complex degrees of freedom afforded by the ability to engineer light-matter interactions at wavelength and sub-wavelength scales. This dissertation investigates key novel degrees of freedom in electromagnetics and photonics, such as topology and nonlocality, which emerge from non-trivial features of the optical response of a material/structure in frequency-momentum domain, and are therefore inextricably linked to the temporal and spatial \textit{dispersion} properties of light in matter. Engineered (meta)materials and metasurfaces have enabled, over the past two decade, a new level of flexibility to realize of a broad range of anomalous optical properties. Most of my work on novel dispersion degrees of freedom has indeed focused on metamaterial platforms, as they provide a fertile playground for these investigations. In particular, in the first two chapters of this dissertation, I discuss topological, nonreciprocal, and chiral plasmonic metamaterials, with a focus on one-way edge (surface) modes, their momentum-space properties, and whether their dispersion diagram is truly unidirectional. I also show how the presence of losses alter momentum-space modal degeneracies and may lead to topological transitions. In the next two chapters, I discuss the relevance of engineering the frequency-dependent and momentum-dependent response of another important class of metamaterial systems, namely, metasurfaces for imaging applications. For instance, a broadband achromatic metalens can be designed by suitably engineering its frequency dispersion, whereas a metasurface with tailored spatial dispersion (nonlocality) can realize momentum-dependent optical functions, such as space-compression effects. Specifically, in this dissertation I discuss the basic principles of these devices and demonstrate their fundamental limitations arising from delay-bandwidth constraints, with respect to relevant performance metrics, particularly bandwidth. The results presented in this dissertation may lead to a better understanding of the intriguing physical effects, practical potential, and fundamental limitations of novel dispersion degrees of freedom in metamaterials and metasurfaces. This may help guide the design of a new generation of electromagnetic and photonic devices for advanced scientific and technological applications.