The quantitative understanding of universal dynamic properties of strongly correlated systems both near and far from equilibrium poses one of the most diverse and challenging problems in contemporary physics. Applications cover a huge range of scales, from low temperature states of condensed matter systems to the extreme states of matter observed, e.g., in ultra-relativistic heavy-ion collisions. Functional methods, e.g., the functional renormalization group and effective action techniques, as well as numerical lattice Monte Carlo methods offer a powerful approach to tackle these problems and to resolve the nonperturbative dynamics. Here, I focus on their applications to critical dynamics in stochastic models with energy conservation as well as universal scaling phenomena in hydrodynamic systems driven far from equilibrium.