The study of lattice vibrations began in the seventeenth century but gained traction with the work of Born and von Kármán on lattice waves through crystalline solids in the early twentieth century. Experimental techniques such as time-of-flight, X-ray diffraction, and neutron diffraction (notably Brockhouse’s constant momentum method) are discussed. Theoretical developments include force constant models and various quantum lattice dynamics theories. Phenomenological models such as the shell model, bond charge model, deformation model, valence charge model and breathing shell model are presented. Among the ab initio methods, the historical developments of augmented plane wave theory, dielectric screening theory, pseudopotential and model potential theories, charge fluctuation model, charge density distortion model, charge density wave model and nonorthogonal tight-binding scheme are presented. Ab initio calculations of electronic susceptibility in transition metals, rare earth metals and their compounds are described in the context of phonon anomalies. It is pointed out that different microscopic theories attribute phonon anomalies to different physical processes going on in transition metals which create some doubts. The chapter also introduces surface phonons, their experimental detection via electron energy loss and helium atom scattering, and theoretical approaches such as the slab and Green’s function methods.