A comprehensive study of the different classes of cycloaddition reactions ([3+2], [2+2], and [2+1]) of SO2 to acetylene and ethylene has been performed using density functional theory (DFT) and composite wavefunction methods. The [3+2] cycloaddition reaction, that was previously explored in the context of the cycloaddition of thioformaldehyde S‐methylide (TSM) to ethylene and acetylene, proceeds in a concerted way to the formation of stable heterocycles. In this paper, we extend our study to the [2+2] and [2+1] cycloadditions of SO2 to acetylene, which would produce 1,1‐oxathiete‐2‐oxide and thiirene‐1,1‐dioxide, respectively. One of the main conclusions is that cyclic 1,1‐oxathiete‐2‐oxide can open through a relatively easy breaking of the SO single bond and rearrange toward sulfinyl acetaldehyde (SA). The SA molecule can easily undergo several internal rearrangements, which eventually lead to sulfenic acid and sulfoxide derivatives of ethenone, 1,2,3‐dioxathiole, and CO plus sulfinylmethane. The most probable path, however, produces 2‐thioxoacetic acid, whose derivatives (or those of the corresponding acetate) are usually obtained by Willgerodt–Kindler‐type sulfuration of acetates. This product can in turn decompose, leading to the final products CO2 and H2CS. Comparison of this decomposition path with that of 2‐amino‐2‐thioxoacetic acid shows that the process occurs through different H‐transfer processes.