Structural disorder typically affects the dynamics of non-equilibrium quantum systems and leads to a variety of unique phenomena that are investigated at extremely low temperatures with new methods. The focus is on the physical realization of such systems in the form of amorphous solids, disordered crystals and spin glasses. Fundamental questions on the interplay of disorder and many-particle interaction, on the microscopic nature of low-lying states, on relaxation and decoherence channels, on dissipative dynamics and on the occurrence of complex collective phenomena are investigated. Current projects focus on the surprising influence of nuclear degrees of freedom on the dynamics of atomic tunnel systems in structurally disordered systems such as multicomponent glasses and polymers. In particular, the nonlinear response and phase coherence of such systems are investigated.