The realization of ultracold quantum gases at Nanokelvin temperatures has marked
a milestone in modern quantum physics. With the help of laser light, these ultracold
atom clouds can be stored in artificial periodic potentials created by laser light - so
called optical lattices - that allow us to explore fundamental aspects of strongly
interacting fermionic and bosonic quantum matter. In very recent experiments, we
have been able to record single snapshots of a quantum fluid in which individual
atoms are detected with single lattice site resolution. This opens unprecedented
novel opportunities for analyzing and manipulating strongly interacting quantum
system. In my talk, I will review some of the recent experiments on strongly
correlated quantum gases in optical lattices and highlight connections to condensed
matter physics, quantum information science and atomic- and molecular physics.