The talk is divided into two parts: in the first, I will talk about dynamics of far-from equilibrium initial states in different lattice models. I will present results of quench dynamics of the XXZ-Heisenberg magnet, where interesting physics emerges after quenching the system. Then I will present results for scattering of solitonic objects in different integrable and non-integrable lattice models. In the second part, I will talk about dynamics of impurity systems. There I will talk about how impurity spectral functions can be calculated using the Chebyshev technique, and how MPS can serve as a high resolution impurity solver for Dynamical Mean-Field Theory. Finally, I will show some results for steady-state currents through a quantum dot device.