Why should a control engineer be interested in singular perturbations of ordinary differential equations? How can some "singular" methods be of help to a system designer in trouble with his "regular" problems? To answer these questions let us remember that one of our most "regular" habits is to simplify mathematical models to be used in system design. A typical simplification is to neglect some "small" time constants, masses, moments of inertia, some "parasitic" capacitances and inductances, and a number of other "unimportant" parameters. There are two good reasons for this simplification. First, inclusion of these parameters increases the dynamic order of the model. Second, inclusion of the parameters introduces "fast modes" which make our model "stiff," that is, hard to handle on a digital computer. There is much to be gained with a simple model but there is also a serious risk: the use of a simplified model may result in a system far from its desired optimum or even an unstable system. If this happens, do we have to repeat the design with a more accurate model? This would be a harsh punishment for taking a reasonable risk. It would be useful to find some less expensive alternatives to improve an oversimplified design. Our intention is to show that the singular perturbation approach provides such an alternative. It will help us to reintroduce the "forgotten" parameters, at a lower cost than if we were to repeat the design. It will also increase our understanding of the consequences of a simplified model. In most applications a singular perturbation method will separately deal with "fast" and "slow modes." In the controller, the part controlling the fast modes will be identifiable as a separate unit. A "two-time scale" implementation of the controller will then reduce the cost of hardware and complexity of software. All these advantages of a singular perturbation method seem "too good to be true." In fact, there are two limitations. In its present form the approach requires good a priori knowledge of small parameters. It is applicable if the parameters are "sufficiently small." While these limitations represent an area of current research, a number of singular perturbation methods can already be employed in the design of optimum control systems and in trajectory optimization problems. The main purpose of this paper is to serve as an introduction to and a preview of the papers in a special session dealing with applications of singular perturbation methods to the design of control systems. This tutorial and somewhat naive outline of singular perturbation methods aimes at conceptual clarity. For a more rigorous discussion of some subtle and intriguing questions a number of mathematical references are recommended.