Cratonic basins are sites of prolonged, broadly distributed but slow subsidence of the continental lithosphere, and are commonly filled with shallow water and terrestrial sedimentary rocks. They remain poorly understood geodynamically. A number of models have been proposed that fall into families involving cooling of stretched continental lithosphere, cooling related to mantle flow (dynamic topography), densification of the underlying lithosphere due to phase changes, the surface response to magmatism and/or plume activity, and long-wavelength buckling under in-plane stresses.The timing of initiation and spatial distribution of cratonic basin formation are linked to geodynamic phases within the overall framework of plate amalgamation and supercontinental break-up and dispersal. Many cratonic basins initiated in the Neoproterozoic and Cambrian-Ordovician. Some suites of cratonic basins originated as broad ramp-like realms of subsidence tilting down to the adjacent passive margin, and were later "individualized" by secondary processes such as, for instance, reactivation of tectonic structures during intracontinental orogeny, and the emergence of intervening arches and domes.Several different mechanisms may therefore control the geological evolution and subsidence history of cratonic basins during their long life-times. We propose that a model of low strain rate extension accompanied and followed by cooling of the underlying lithosphere satisfactorily explains the long-term subsidence history of a range of cratonic basins. However, the precise role played by dynamic topography transmitted from large-scale mantle flow in initiating or modifying the elevation history of continental interiors remains an intriguing focus for further research.