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In the age of miniaturization where the physical systems approach the nanoscale limit andwhere more complex materials are created there is necessity for understanding in terms ofquantum mechanics. The understanding then opens and gives possibilities for manipulationand engineering of such systems and thus practical applications.Quantum mechanics states that the electron cannot be characterized as In this thesis we focus on improvements of the description of the electron-electron correlation effects in nonequilibrium nanosystems. We mainly focus on developments of two nonequilibrium methods, namely the formalism of Nonequilibrium Green’s Function and Time Dependent Density Functional Theory and we explore the possibility to improve existing approximations in these theories. A smaller part o