In recent years, research at the interface of chemistry, material science, condensed matter physics, quantum electrodynamics, and quantum optics has surged and now opens a new pathway to control materials properties using quantum light. In this project, we explore the complex static and dynamical behavior of light-matter interactions beyond classical limits of molecular and solid-state systems that are embedded in cavities, metamaterials, or nanoplasmonic structures, both in weak and strong-coupling regimes. In the strong-coupling limit, the light and matter lose their identities, and novel hybridized states of light and matter are formed, e.g., polaritons or plasmon-polaritons or others will emerge. Those new hybridized states that emerge from the strong light-matter coupling limit provide novel ground for designing a wealth of new functional materials. We describe these systems using a unified density-functional framework (quantum-electrodynamical density-functional theory QEDFT), where light and matter can be treated on the same footing. Our work includes methods development, as well as the study of the effects of strong light-matter coupling on chemical reactions, spectroscopy, electron-phonon and phonon-phonon interactions, condensation, and cavity-mediated superconductivity.