The dissociative adsorption of molecular hydrogen on silicon is considered to be the prototype for an activated chemical reaction at a semiconductor surface. The covalent nature of the silicon–silicon and silicon–hydrogen bonds lead to large lattice distortion in the transition state of the reaction. As a result, the apparently simple reaction exhibits relatively complex pathways and surprisingly rich dynamics. The report reviews, among others, experiments using optical second-harmonic generation, molecular beam techniques and scanning tunnelling microscopy which, in close connection with state-of-the-art density functional theory, have led to a detailed microscopic understanding of H2 adsorption on Si(001) and Si(111) surfaces. On the dimerized Si(001) surface, dissociative adsorption as well as recombinative desorption of H2 is shown to involve the dangling bonds of two neighbouring dimers. Preadsorption of atomic hydrogen or thermal excitation is able to substantially alter the adsorption barrier. As a consequence, the reactivity strongly depends on coverage and surface temperature. In contrast to activated adsorption of hydrogen at metal surfaces, even the most basic description of the dynamics has to include phonon excitation of the silicon substrate.