Structure prediction of stable and metastable polymorphs of chemical systems in low dimensions has become an important field, since materials that are patterned on the nano-scale are of increasing importance in modern technological applications. While many techniques for the prediction of crystalline structures in three dimensions or of small clusters of atoms have been developed over the past three decades, dealing with low-dimensional systems—ideal one-dimensional and two-dimensional systems, quasi-one-dimensional and quasi-two-dimensional systems, as well as low-dimensional composite systems—poses its own challenges that need to be addressed when developing a systematic methodology for the determination of low-dimensional polymorphs that are suitable for practical applications. Quite generally, the search algorithms that had been developed for three-dimensional systems need to be adjusted when being applied to low-dimensional systems with their own specific constraints; in particular, the embedding of the (quasi-)one-dimensional/two-dimensional system in three dimensions and the influence of stabilizing substrates need to be taken into account, both on a technical and a conceptual level.This article is part of a discussion meeting issue ‘Supercomputing simulations of advanced materials’.