The article provides a comprehensive theoretical and experimental review of surface plasmons and surface-plasmon polaritons, focusing on the collective electronic excitations at metal surfaces. It covers the classical approach to surface plasmons, including the surface-plasmon condition, energy dispersion, and skin depth in semi-infinite systems and thin films. The nonretarded surface plasmon is discussed using simplified models, such as the planar surface plasmon and localized surface plasmons, with detailed analyses of classical models, nonlocal corrections, and hydrodynamic approximations. The article also explores the boundary-charge method for determining the frequencies of localized surface plasmons in complex geometries and the effective-medium approach for composite systems. Additionally, it reviews the dynamical structure factor, density-response function, inverse dielectric function, and screened interaction, including classical and nonlocal models. The article further examines the surface-response function, including the generation rate of electronic excitations, inelastic electron scattering, and the properties of surface plasmons in jellium and real surfaces, as well as acoustic surface plasmons. Finally, it discusses applications in particle-surface interactions, scanning transmission electron microscopy, and plasmonics, highlighting the potential of surface plasmons in nanoscale photonics and electronics.The article provides a comprehensive theoretical and experimental review of surface plasmons and surface-plasmon polaritons, focusing on the collective electronic excitations at metal surfaces. It covers the classical approach to surface plasmons, including the surface-plasmon condition, energy dispersion, and skin depth in semi-infinite systems and thin films. The nonretarded surface plasmon is discussed using simplified models, such as the planar surface plasmon and localized surface plasmons, with detailed analyses of classical models, nonlocal corrections, and hydrodynamic approximations. The article also explores the boundary-charge method for determining the frequencies of localized surface plasmons in complex geometries and the effective-medium approach for composite systems. Additionally, it reviews the dynamical structure factor, density-response function, inverse dielectric function, and screened interaction, including classical and nonlocal models. The article further examines the surface-response function, including the generation rate of electronic excitations, inelastic electron scattering, and the properties of surface plasmons in jellium and real surfaces, as well as acoustic surface plasmons. Finally, it discusses applications in particle-surface interactions, scanning transmission electron microscopy, and plasmonics, highlighting the potential of surface plasmons in nanoscale photonics and electronics.