Abstract Recent theoretical and observational advances in understanding the dynamics of lithosphere processes have yielded strong evidence in favour of the existence of large-scale lithosphere folds. Intraplate compressional stresses generated by plate tectonic forces can reach magnitudes that approach the plastic buckling strength of mechanical models of lithosphere with brittle-ductile rheological stratification. The models predict lower plastic buckling stresses for continental lithosphere than for oceanic lithosphere. Intraplate folding of relatively strong oceanic lithosphere, documented extensively in the northeastern Indian Ocean, occurs where stresses are concentrated by restricted geometric and dynamic conditions resulting in unusually high stress levels (several hundreds MPa). On continents, where geophysical data suggest that lithosphere folding may have occurred during the development of sedimentary basins in northern Canada and central Australia, buckling stresses can have magnitudes that are of a similar order to those thought typically to occur in the lithosphere (several tens MPa). Folding of continental lithosphere, although more difficult to document, is likely to be an important mechanism of large-scale continental deformation. In particular, thinned continental lithosphere, with a history of superposition of thick sedimentary successions, might be the preferential locus of such folding. Lithosphere folding could also be a controlling factor in the near-surface deformation of rifted basins as reflected by tectonic basin inversion.