Singular perturbations occur when a small coefficient affects the highest order derivatives in a system of partial differential equations. From the physical point of view, singular perturbations generate thin layers located near the boundary of a domain, called boundary layers where many important physical phenomena occur. In this talk, we introduce a methodology, based on the utilization of correctors as proposed by J.-L. Lions and R. Temam, and use systematically this method of correctors to analyze the boundary layers of certain classes of singular perturbation problems. We consider first elliptic and parabolic equations in a bounded domain, and then a number of problems in fluid mechanics. Some related applications in numerical computations are briefly discussed as well.