Based on the works [R1] - [R10], this thesis tackles various aspects of the dynamics of interacting quantum many-body systems. Particular emphasis is given to the understanding of transport and thermalization phenomena in isolated (quasi) one-dimensional quantum spin models. Employing a variety of methods, these phenomena are studied both, close to equilibrium where linear response theory (LRT) is valid, as well as in far-from-equilibrium situations where LRT is supposed to break down. The main results of this thesis can be summarized as follows. First, it is shown that conventional hydrodynamic transport, i.e., diffusion, occurs in a number of (integrable and nonintegrable) quantum models and can be detected by looking at different signatures in position and momentum space as well as in the time and the frequency domain. Furthermore, the out-of-equilibrium dynamics resulting from a realistic class of initial states is explored. These states are thermal states of the model in the presence of an additional static force, but become nonequilibrium states when this force is eventually removed. Remarkably, it is shown that in some cases, the full time-dependent relaxation process can become independent of whether the initial state is prepared close to or far away from equilibrium. In this context, a new connection between the eigenstate thermalization hypothesis and linear response theory is unveiled. Finally, this thesis also reports progress on the development and improvement of numerical and (semi-)analytical techniques to access the dynamics of quantum many-body systems. Specifically, a novel combination of dynamical quantum typicality and numerical linked cluster expansions is employed to study current-current correlation functions in chain and ladder geometries in the thermodynamic limit.