Summary: This paper presents an overview on results in averaging theory. First, averaging for ordinary differential equations is presented. These results are then applied to fast oscillating differential equations to show how zero perturbations can affect stability properties. Next, averaging for functional-differential equations (FDEs) is presented. A comparison of ‘classical’ averaged models and more recently developed averaged models for FDEs is given. Then the FDE averaging results are applied to fast oscillating delay differential equations. It is explained that fast oscillating FDEs are often sensitive to extremely small delays. Several examples are presented in this paper to help give an overview on results.