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The quantum mechanical description of (laser-driven) electron dynamics in molecular and solid-state systems is of relevance for molecular and nanoelectronics, photoche- mistry, and spectroscopy. Here, explicitly time-dependent methods in one-electron approximation (wavepacket propagation or open-system density matrix theory with relaxation and dephasing terms), and explicitly time-dependent correlated many- electron methods (TD-CI, Time-Dependent Configuration Interaction, and MCTD- HF, Multi-Configurational Time-Dependent Hartree-Fock) are developed and used. For transport problems, also the Landauer formalism is adopted. Specific examples are (numbering refers to publication list):