Rolf Huisgen explored the Diels–Alder reactions of 1,3,5‐cycloheptatriene (CHT) and cyclooctatetraene (COT) with the dienophiles maleic anhydride and 4‐phenyl‐1,2,4‐triazoline‐3,5‐dione (PTAD) to determine the kinetics and mechanisms of various electrocyclizations and Diels–Alder reactions. These reactions have been examined with density functional theory. Modern computational chemistry has provided information not previously available by experiment. Transition states for all the reactions have been identified, and their Gibbs energies are used to explain the experimental reactivities. Zwitterionic intermediates were not found in the [4+2] cycloadditions of both CHT or COT with PTAD and are thus not involved in these reactions. [2+2+2] cycloadditions, as an alternative path to the Diels–Alder products, are highly disfavored. Rapid double nitrogen inversion was found for the cycloaddition products with PTAD.