Dynamical processes set yet another degree of complexity to the many-body problem. With the advent of ultrafast measuring techniques modern experiments often leave the regime of adiabaticity or linear response. The evolution of quantum systems on short time scales subject to strong disturbances then becomes relevant. In this contribution, I will present two different examples that demonstrate aspects of non-equilibrium dynamics in many-body quantum systems. The first example considers the temporal evolution of a closed many-body-system represented by a simple molecule being exposed to a strong ionizing light pulse. Solving the time-dependent Schrödinger equation reveals different processes in the charge dynamics following ionization. It will be demonstrated that a proper choice of electron-hole excitations is crucial for capturing the essential physics. The second example features the non-equilibrium dynamics of an open quantum system. The spin of a magnetic ad-atom residing on the surface of a non-magnetic substrate is exposed to the tunneling current of a scanning tunneling microscope. Spin torque of the tunneling electrons induces spin-dynamics of the surface spin. A master-equation approach is used to solve von-Neumann's equation of motion for the reduced density matrix of the surface spin. Challenges in computing the short time dynamics of the system by different methods are being exhibited.