The ordinary theory of hydrodynamics, while extremely successful, does not account for the inherently random nature of our universe, both quantum and thermal. When carefully accounted for, these effects can modify the qualitative predictions of hydrodynamics for non-equilibrium phenomena. They are particularly important when studying physical scenarios that operate naturally out of equilibrium. Examples include critical phenomena, active and biological matter, astrophysical processes, etc. Schwinger-Keldysh hydrodynamics is a recently-developed theoretical framework to systematically include random stochastic processes into the universal theory of hydrodynamics.