We investigate the many-body physics of ultracold gases of bosonic atom both in and out of equilibrium. Coherent dynamics and thermalization, high-order correlations and their control – all these subjects are at the focus of our theoretical studies. For the numerical solution of the time-dependent many-body Schrödinger equation, we use the MultiConfigurational Time-Dependent Hartree approach for indistinguishable bosons or fermions (MCTDH-X). Our theoretical studies are inspired by and aimed to support the current experimental activities at the Atomchip group.