Mesoscopic electrodynamics at metal surfaces: - from quantum-corrected hydrodynamics to microscopic surface-response formalism

Plasmonic phenomena in metals are commonly explored within the framework of classical electrodynamics and semiclassical models for the interactions of light with free-electron matter. The more detailed understanding of mesoscopic electrodynamics at metal surfaces is, however, becoming increasingly important for both fundamental developments in quantum plasmonics and potential applications in emerging light-based quantum technologies. The review offers a colloquial introduction to recent mesoscopic formalism, ranging from quantum-corrected hydrodynamics to microscopic surface-response formalism, offering also perspectives on possible future avenues.