Orbital physics in correlated electron systems

Orbital degrees of freedom bring about rich and colorful quantum phases in correlated electron systems of condensed matter, and lead to complexity, hence challenging our understanding of the nature of strongly correlated systems. In this review the various properties of multi-orbital correlated electron systems are introduced: we first briefly describe the important role of the orbital degrees of freedom and the scenario of orbital order; next we discuss the inter-relationship among orbital polarization, orbital ordering and lattice distortion in some classical orbital-ordered compounds, and outline the theories and experiments on detecting orbital order; then we introduce the magnetic modulation of multi-orbital metal-insulator transitions and multi-orbital superconductivity;finally we discuss the present problems and challenges in the research of orbital physics.