The far-from-equilibrium dynamics of closed quantum systems has become a central topic in condensed matter physics, due to incredible experimental advances in cold atomic and other systems. Concepts of quantum information have taken center stage in this context, with entanglement, in particular, playing a central role in the emergence of thermodynamics. Predicting the behavior of these quantities, however, is notoriously hard as most existing analytical and numerical tools, designed for systems in equilibrium, do not carry over to the dynamical setting. In my talk I will discuss how studying a set solvable minimal models has allowed us to partially conquer this problem and uncover universal features of quantum dynamics. In particular, I will describe some simple hydrodynamic models of how quantum information spreads in time, and discuss a recent prediction for entanglement growth that is particularly relevant for cold atom experiments.