We consider the singularly perturbed boundary value problems for which the boundary layers are described by exponential functions. The application of classical methods to obtain their approximatie solutions does not give satisfactory results. Hence, it is necessary to adapt the methods to the properties of exponential functions. We give a survey of the known procedures of adapting discrete and global methods. A new adaptation procedure is proposed for Shishkin meshes yielding uniform convergence of spline collocation procedures.