This research proposal addresses non-equilibrium processes occurring in one-dimensional quantum fluids. The interest to this area has surged in recent years due to the rapid development of fabrication and measurement techniques in nanophysics and physics of ultra-cold atomic gases. Nanoelectronics devices (such as quantum point contacts, nanotubes and organic nanowires) and ultracold gases in elongated optical traps are the experimental systems where one-dimensional quantum fluids are encountered. While the main focus of nanoelectronics has always been on the electrical and spin transport, with only limited access to other aspects of non-equilibrium dynamics, the amazing degree of control over atomic systems has transformed the physics of one-dimensional fluids into a rapidly expanding universe of non-equilibrium phenomena. Quantum quenches, explosions and collisions of atomic clouds, diffusion and drift of quantum impurities, motion and decay of solitary waves have been observed and mapped in real time measurements. The fundamental value of the research in this direction lies in the strongly correlated nature of one-dimensional quantum systems, which makes their kinetic theory a largely unexplored territory. For these systems, the application of traditional tools of the kinetic theory, such as the Boltzmann collision integral and non-linear equations of hydrodinamics meets with serious conceptual difficulties. Indeed, it is usually impossible to represent the low-energy excitations of a one-dimensional system as a collection of weakly interacting quasiparticles. It is also impossible to consistently quantize non-linear hydrodynamcis within the standard framework of perturbative quantum field theory. The main goal of this project is to develop methods bypassing these difficulties and to formulate a theoretical framework suitable for the description of non-equilibrium phenomena in one dimension.