In the most general terms, a cycloaddition reaction is one that forms a ring from multiple π-bonds. To illustrate some of the concepts and ways that these reactions are classified, let’s look at the cycloaddition reaction shown below. This reaction, known as the Diels-Alder reaction, is between a conjugated diene (double alkene) and a another alkene that likes to react with dienes (hence dienophile, or diene lover). It is classified as a [4 + 2] cycloaddition, referring to the number of atoms directly involved in bond-forming events.

(There’s a second system for classifying cycloaddition reactions that uses the number of π-electrons involved in ring formation, but let’s just leave that aside.)