Trends in Ultracold Atom Gases: Disordered Systems and Relaxation Dynamics In recent years, ultracold atom gases in optical lattices have provided a unique new playground for the study of strongly interacting quantum systems. Beyond the very interesting study of phenomena also found in solid state systems (quantum phase transitions, Mott insulators, etc.), a particularly nice feature is the amount of control over the lattice potentials, both spatially and temporally. On the one hand, this allows highly detailed studies on the interplay of disorder and interaction, e.g. in bichromatic optical lattices, with interesting analogies, but also strong differences to the physics in "conventional" disordered systems, e.g. with box disorder. On the other hand, tunability of interactions and effectively very weak interactions with the environment allow to address theoretically and experimentally the question how closed quantum systems may perform a semblance of thermalization at the level of subsystems. Here I will present a setup that is currently under experimental study which resolves the problem of studying local relaxation when only global measurements of the system are possible.