A generic interacting and thermalizing classical or quantum many-body system exhibits a hydrodynamic limit, where at late times the dynamics is entirely controlled by collective modes of locally conserved quantities.  A hydrodynamic perspective gives a simple, solvable limit of the transport problem in a strongly correlated electron system.  I will describe the consequences of hydrodynamics on the DC electrical and thermal conductivity, highlighting three particular examples we have recently studied: (1) the consequences of potential vs. magnetic disorder on transport in viscous Fermi liquids, (2) consequences of Fermi surface geometry on transport at the ballistic-to-hydrodynamic crossover, and (3) the experimentally observed violations of the Wiedemann-Franz law in the quasirelativistic electron-hole plasma of graphene.  These new theories may explain puzzling transport phenomena, including T^2 resistivity in single-band SrTiO3, and "strange metal" phases.