Ultracold atomic physics experiments offer a nearly ideal context for the investigation of quantum systems far from equilibrium. I will present first results from two new experiments investigating driven quantum gases. The first experiment aims to realize a nontrivial Floquet phase of matter in a strongly amplitude-modulated optical lattice. The new phase can be understood as a many-body quantum-mechanical analogue of an inverted Kapitza pendulum. The second experiment uses trapped degenerate strontium as a quantum emulator of ultrafast atom-light interactions. Here the low energy scales of cold atom experiments give rise to an effective temporal magnification factor of eleven orders of magnitude, enabling the study of nonequilibrium dynamics relevant to attosecond-scale electronic phenomena.