Convection-dominated problems, where diffusion is also present, arise in the modelling of various physical processes. Typically their solutions exhibit boundary and/or interior layers. In general it is not easy to devise numerical methods that yield accurate computed solutions for this class of problems.

In this talk the fundamental properties of the solutions of convection-diffusion problems will be presented. When standard numerical methods are applied to these problems, it will be shown that one obtains unsatisfactory computed solutions. Thus special numerical techniques are used for their solution; some of these (including Shishkin meshes) will be described. 
