The physics of systems out of equilibrium represents a fascinating chapter of science, with many unsolved problems and unexplored issues. Quantum gases are particularly well suited to investigate non-equilibrium phenomena, because the key parameters of the problem (scattering length, trapping conditions, etc.) can be varied in a well controlled manner. They also offer unique opportunities to perform experimental measurements with high precision. This project aims to theoretically explore novel dynamic and transport properties of quantum gases at both finite and zero temperature, with special emphasis on the effects of quantum statistics, superfluidity and the role of interactions. The major goal is to achieve a deeper understanding of several fundamental issues: the universal properties exhibited by dilute quantum gases; the role of viscosity in non-uniform configurations; the applicability of quantum Monte Carlo techniques to explore the dynamics and transport properties of Bose and Fermi gases; the concept of superfluidity in systems far from equilibrium; the motion of impurities embedded in quantum baths, their interaction and the consequences on the dynamic behaviour; the collective excitations exhibited by novel quantum phases like binary mixtures of quantum gases and dipolar atomic and molecular gases; the effects of disorder; the condensed matter analogues of gravitational physics; the study of self-trapping and Josephson oscillations in superfluid Bose and Fermi gases. An important motivation of the project is to identify questions of broad interest which might be relevant also beyond the realm of quantum gases, as well as to develop advanced theoretical approaches to challenging problems of statistical mechanics and many-body physics.