Dimer models arise as effective descriptions in a variety of physical contexts, and provide paradigmatic examples of systems subject to strong local constraints. Their statistical mechanics exhibits unusual phenomena such as algebraic correlations and deconfinement of monomer excitations. I will first describe the classical non-equilibrium dynamics of the dimer model, where signatures of strong correlations are visible in both global and local observables, and can be understood in terms of one-dimensional strings of high mobility. I will then show how the classical dynamics can be used to study the corresponding quantum problem, and helps to resolve an outstanding puzzle about the structure of the phase diagram.