Macroscopic quantum systems with many interacting particles can display novel emergent phenomena, ranging from exotic superconductors to topological insulators. Traditionally, many-body systems were most easily studied – conceptually and experimentally – near low temperatures and thermal equilibrium. A confluence of interdisciplinary developments, particularly experimental advances in building programmable quantum devices, have opened up completely novel regimes for many-body physics: highly excited, quantum-coherent and far-from-equilibrium. My research aims to advance many-body theory into the uncharted domain of non-equilibrium quantum dynamics using a variety of analytic, numerical and information theoretic approaches. My work has pioneered frameworks for defining nonequilibrium phases of matter, including discovering the time-crystal, a phase that is disallowed in equilibrium, but has a sharp dynamical realization.