Abstract: Atoms trapped in optical lattices are versatile systems that can be used to model many-body systems, as quantum computing resources, and for precision measurements. I will explain in general how such experiments work, and describe in particular our experiments at Penn State. The focus of the talk will be predominantly on 1D Bose gases, which can provide unique insights into the foundations of quantum statistical mechanics. Other experiments will also be mentioned, like trapping arrays of single atoms on the road to making a quantum computer.