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Novel physics arises when strongly correlated system is driven out of equilibrium by external fields. Dramatic changes in physical properties, such as conductivity, are empirically observed in strongly correlated materials under high electric field. In particular, electric-field driven metal-insulator transitions are well-known as the resistive switching effect in a variety of materials, such as VO$_2$, V$_2$O$_3$ and other transition metal oxides. To satisfactorily explain both the phenomenology and its underlying mechanism, it is required to model microscopically the out-of-equilibrium dissipative lattice system of interacting electrons. In this thesis, we developed a systematic method of modeling non-equilibrium steady states for dissipative lattice systems by means of Non-equilibrium Green's function and Dynamical Mean Field Theory. We firstly establish a "minimum model" to formulate the strong-field transport in non-interacting dissipative electron lattice. This model is exactly soluble and convenient for discussing energy dissipation and steady-state properties. The formalism is then combined with Dynamical Mean Field Theory to provide a systematic framework describing the nonequilibrium steady-state of correlated materials. We use the formalism to study the strong-field transport properties of correlated materials, Mott insulators and Dirac electrons in graphene. We concentrate on the microscopic description of resistive switching. Of particular interest is the filament formation during the dynamical phase transition, which has been interpreted as a result of the delicate interplay between dissipation and Mott physics. We will also examine $IV$ characteristics and particularly the current saturation of Dirac electrons in graphene. The arXiv version has been updated with minor modifications and corrections.