In this Focus Review, we present the application of the so-called Activation Strain Model of chemical reactivity to the Diels-Alder cycloaddition reaction. To this end, representative recent examples have been selected to illustrate the power of this new computational approach to gain a deeper quantitative understanding of this fundamental process in chemistry. We cover a wide range of issues, such as, the "endo-rule", reactivity trends emerging from systematic variation in the reactants' strain, and cycloaddition reactions involving relevant species in material science, that is, fullerenes, polycyclic aromatic hydrocarbons and nanotubes.