Complex quantum systems out of equilibrium are at the basis of a
number of the most intriguing puzzles in physics. This talk will be
concerned with recent progress on understanding how quantum many-body
systems out of equilibrium eventually come to rest and thermalise. The
first part of the talk will highlight theoretical progress on this
question, taking in several ways a quantum information view -
employing ideas of Lieb-Robinson bounds, quantum central limit
theorems and of concentration of measure. These findings will be
complemented by experimental work with ultra-cold atoms in optical
lattices, in setups constituting dynamical "quantum simulators",
allowing to probe physical questions that are not only out of reach
for state-of-the-art numerical techniques based on matrix-product
states, but also relate to classically computationally hard problems.