Seven fundamental questions on the relationship of lithospheric stresses and sedimentary basin origin and evolution are posed and elaborated. These are: (1) How is the evolution of sedimentary basins tied to lithospheric dynamics? (2) What are the sources of stress that lead to formation of sedimentary basins? (3) How does the interaction between internally and externally applied stresses affect the formation and evolution of sedimentary basins? (4) How do space and time variations of rheology and pore pressure affect stress transmission, strain, vertical motions, and stratigraphy during basin evolution? (5) What factors influence spatial and temporal variations of rheology in, and around, different kinds of sedimentary basins? (6) What is the role of magmatism in basin formation and what deep-seated processes does it reflect? (7) What is the relationship between basin evolution, thermal history, and fluid flow? These fundamental questions can be investigated by developing fully-dynamic models of processes at the basin and sub-basin scale. Models must incorporate or honour basin history and plate reconstructions; the intregration of structural and sedimentological data; direct observations of the physical state; and the synthesis of geological and geophysical data, including tectono/dynamic stratigraphy, petrological and geochemical data, and geophysical data (gravity, magnetics, heat flow, deep and shallow seismics). A number of type basins - in passive margin, foreland, rift, and strike-slip tectonic settings - suitable for modelling studies elucidating the fundamental questions are identified.