Recently the understanding and control of spin-orbit coupling have become subjects of intensive research across many different disciplines in condensed matter physics. In particular, spin-orbit coupling in correlated electron materials has been recognized for its role in creating a new class of electronic states that allow crossed-responses of the electrons to electric and magnetic fields. This is especially the case when the spin, orbital, and lattice energy scales are comparable, so that the interplay between different degrees of freedom allows the emergence of novel many-body states and their crossed-responses to external probes. Several new collective states of matter have been proposed in this context, including novel spin-orbital ordered states, correlated topological insulators, topological superconductors, quantum spin liquids, topological semi-metals, and multipolar ordered phases. At the same time, theoretical and experimental efforts are underway to predict and measure elementary excitations of such systems. Equally important is the availability of the increasing number of new quantum materials with significant spin-orbit coupling, including several new 5d transition metal oxides (iridates, osmates etc), multiferroic materials, and heterostructures of transition metal systems.