Ultracold quantum gases offer novel and intriguing possibilities to probe the dynamical evolution of strongly correlated quantum systems far from equilibrium. In the talk, I will report on recent experiments, in which we have probed the quantum dynamics of 1D ladder systems far from equilibrium. We have especially focussed on how fundamental quantum mechanical concepts such as Landau-Zener transitions can be extended into the many-body regime, and are influenced by the interactions between the particles. Finally, I will report in more detail on our recent efforts to image and address single atoms in optical lattices. I will show how we are we able to structure the quantum gases and probe correlation properties and remove entropic regions of the quantum gas in the lattice — an essential part of novel cooling strategies. Furthermore, I will report on first results on how coherent light scattering from only few atoms can be used to reveal spin ordering in a lattice.