We review the dynamics of supercooled liquids approaching the liquid-glass transition, starting with the conventional generalized hydrodynamics formulation. Empirical models for the memory function are discussed, as are empirical models for the self-energy function for phonons in crystals. Two examples of microscopic analyses based on non-linear interactions are then described, the anharmonic lattice dynamics model for structural phase transitions, and Kawasaki's mode-mode-coupling approach for critical dynamics. We then review the mode-coupling theory of the liquid-glass transition, emphasizing its relation to generalized hydrodynamics with the memory function derived from a microscopic theory of non-linear interactions. We discuss the major predictions of this theory, particularly the asymptotic expansion results, which provide specific formulae for analysing experimental data.