The proposal is to study non-equilibrium states of strongly correlated quantum systems relevant for heavy ion and condensed matter physics by using existing and developing new methods of gauge-string duality (also know as holography or AdS/CFT correspondence). The gauge-string duality is a set of non-perturbative tools developed within string theory over the last fourteen years. These methods can be used independently of the final status of the string theory itself. Strongly coupled model systems at finite temperature and density are of great interest for they appear in many areas of physics including physics of heavy ion collisions and physics of trapped cold atoms. Gauge-string duality methods already proved very useful in supplying information about transport properties such as viscosity and spectral functions of thermal quantum field theories at strong coupling.Specific goals of the proposal are divided into two sets, one including open problems in non-equilibrium systems accessible for study by the existing gauge/string duality techniques, and another involving more challenging problems requiring new holographic approaches. Problems of the first set include generalizing existing models of thermalization and isotropization, constructing simple model(s) describing the initial state of the quark-gluon plasma, exploring gravity backgrounds obtained by self-consistent top-down approach, studying theories with dual gravity backgrounds including full back-reaction. Problems of the second set involve holographic approach to turbulence and plasma instabilities, building holographic formalism for highly nonequilibrium processes and studying possible connection between holography and emergent gravity.