Ultra-short laser pulses can be used to initiate, manipulate, and control coherent electron dynamics. A wealth of physical processes and novel quantum phenomena can be explored, such as topological states, Floquet physics, coherent exciton Bose-Einstein condensation, and spin precession driven by coherent magnons in quantum materials. For example, in biological systems, charge migration can be enhanced by coherent dynamics of phonons and electrons. This phenomenon, already seen in photosynthesis, is of central importance for designing efficient organic opto-electronic devices. All these involve energetically excited states that gradually lose coherence via interaction with the environment. This constitutes a major limiting factor for realizing quantum-computing material designs, stabilizing light-driven topological states (Floquet topology), or allowing exciton condensates in condensed matter. The TIMES network will face the challenge of understanding and predicting the coupled and coherent electron-phonon dynamics of quantum states. The developed theoretical approaches, in collaboration with experimental partners will push the boundaries of the current simulations of out-of-equilibrium phenomena.