Zeolites are nanoporous aluminosilicates with well-defined crystalline structures, considered key assets in heterogeneous catalysis, with a broad range of industrial applications. Computational investigations dealing with zeolite catalysts have been undertaken for decades with simple models of the bulk sites, known to be bridging Si IV −OH−Al IV groups, in the case where the compensation cation is a proton. Real zeolite catalysts used in practice are however finite size and intricate objects, with external surface sites and defects, among other sources of complexity. Amorphous silica−alumina may also be obtained as a consequence of zeolite post-treatments or synthesized on purpose to obtain acid sites that are milder than those of zeolites. In the present Perspective, some of the achievements in the field of the atomic-scale simulation of intricate aluminosilicate catalysts (zeolites, amorphous silica−aluminas) of industrial relevance are reviewed. Emphasis is put on the simulation of the mechanisms of post-treatments of zeolites, and on the special structure and reactivity of acid sites at external surfaces of zeolites and on amorphous silica−alumina, that is shown to differ from the properties of the bulk bridging sites. Moreover, directions for future investigations are proposed.