Quantum many-body physics has traditionally been dominated by detailed investigations of equilibrium properties and low-energy excitations. In the last decade or so, motivated by novel experimental possibilities such as cold atoms, the study of quantum matter far from equilibrium has emerged as an important and exciting new field. I will start with a selection of new questions and phenomena that have appeared in the context of non-equilibrium evolution in isolated systems. I will end by focusing on a specific example, namely, the dynamics of composite objects in lattice systems. such as repulsively bound pairs, triplets and clusters.