This article reviews recent progress in understanding the dynamics of molecular dissociation in impact on crystalline surfaces, a topic pursued by a combination of theoretical methods (trajectory calculations and impulsive collision models) with molecular beam scattering experiments. The studies reviewed deal with molecules such as I2 and ICl in collision with single-crystal surfaces of chemically inert insulators, e.g., MgO(100), sapphire, and diamond. Dissociation in such systems is an elementary, single-collision process, advantageous for pursuing understanding on a first-principles basis. The main findings include the following: (1) Dissociation occurs by a centrifugal mechanism involving high rotational excitation upon impact. (2) Large energy transfer to the solid takes place in cases such as I2/MgO(100) and I2/sapphire, the mechanism of which is shown by theoretical simulations to involve a shock-wave excitation of the solid upon the molecular impact. The effect of energy transfer to the solid on the dissociation probability depends strongly on the system, and the theoretical model provides an interpretation for this. (3) There are important qualitative differences between the results for a homonuclear collider and those for a related mass asymmetric molecule (e.g., I2 vs. ICl) regarding the energy dependence of the dissociation probability and the energy distribution of the products. It is argued that for the simplest systems studied a coherent picture seems to emerge for the various aspects of the dissociation process with good consistency between theoretical and experimental results. Major open problems and future directions in the field are discussed.