The hypothesis of local equilibrium is central in non-equilibrium thermodynamics. We define and review support for this hypothesis for three-, two- and one-dimensional, macroscopic thermodynamic systems. The hypothesis can also be supported in mesoscopic systems. It does not apply to density-gradient theories as these introduce nonlocal variables, but is found to apply if we define surface excess variables according to Gibbs. The hypothesis can therefore be actively used to predict surface properties.