  Inelastic light scattering is an intensively used tool in the study of
electronic properties of solids. Triggered by the discovery of high temperature
superconductivity in the cuprates and by new developments in instrumentation,
light scattering both in the visible (Raman effect) and the X-ray part of the
electromagnetic spectrum has become a method complementary to optical
(infrared) spectroscopy while providing additional and relevant information.
The main purpose of the review is to position Raman scattering with regard to
single-particle methods like angle-resolved photoemission spectroscopy (ARPES),
and other transport and thermodynamic measurements in correlated materials.
Particular focus will be placed on photon polarizations and the role of
symmetry to elucidate the dynamics of electrons in different regions of the
Brillouin zone. This advantage over conventional transport (usually measuring
averaged properties) indeed provides new insights into anisotropic and complex
many-body behavior of electrons in various systems. We review recent
developments in the theory of electronic Raman scattering in correlated systems
and experimental results in paradigmatic materials such as the A15
superconductors, magnetic and paramagnetic insulators, compounds with competing
orders, as well as the cuprates with high superconducting transition
temperatures. We present an overview of the manifestations of complexity in the
Raman response due to the impact of correlations and developing competing
orders. In a variety of materials we discuss which observations may be
understood and summarize important open questions that pave the way to a
detailed understanding of correlated electron systems.
