Abstract: Ultracold atoms in optical lattices are one of the major platforms for experimental quantum simulations and many-body physics. Their versatile nature and high controllability enable the realization of novel quantum phases, the study of phase transitions, and the observation of non-equilibrium dynamics. In the past, most experiments studied these phenomena in the simplest lattice geometries, namely the primitive 1D lattice, the square lattice, and the cubic lattice. In this talk, we will look at many-body physics in other interesting 2D lattice geometries. These range from the triangular lattice, where geometric frustration can give rise to chiral superfluids, over the Kagome lattice, where it gives rise to a flat band, to optical quasicrystals. In quasicrystals, which are a novel form of condensed matter that is not periodic but nonetheless long-range ordered, the notion of band structure is not directly applicable. Here I will present both our experimental realization of the 2D Bose glass as well as novel work.