Ultracold atoms in optical lattices, bosons and more recently also fermions, have enjoyed much experimental attention in recent years. They allow for the application of many concepts inspired by solid state physics. Recent experiments in our lab both focus on the transitions to different Fermionic and Bosonic insulator states themselves as well as using them as an initial state for experiments e.g. on quantum information or atomic interaction properties. We show one of the fundamental aspects of the bosonic Mott insulator state, its incompressibility, by directly detecting the predicted “shell structure” in the density districution. These characteristic concentric shells have internally constant densities and sharp boundaries in between. Furthermore, coherent coupling of the on-site vibrational levels with Raman transitions allows for the efficient transfer into the excited bands of the lattice potential along any desired direction. Atoms in such a state are expected to have modified interaction properties and have additional effectively internal degrees of freedom, which are interesting for more complex quantum phases such as multi-flavour models or supersolids.