According to the author, asymptotic preserving (AP) schemes are schemes that are efficient in these asymptotic regimes. The designing principle of AP schemes is to preserve, at the discrete level, the asymptotic limit that drives one (usually the microscopic) equation to its asymptotic (macroscopic) equation. In this paper, the author reviews the basic theory and methods, and gives several representative examples of asymptotic preserving schemes. Most examples are kinetic and hyperbolic equations. The concept also applies to many other equations that admit asymptotic structures.