We survey the general methodology in developing asymptotic preserving schemes for physical problems with multiple spatial and temporal scales. These schemes are first-principle based, and automatically become macroscopic solvers when the microscoipic scales are not resolved numerically. They avoid the coupling of models of different
scales, thus do not face the difficult task of transfering data from one scale to the other as in most multiscale methods. These schemes are very effective for the coupling of kinetic and hydrodynamic equations, and problems with fast reactions.