We review results on combined stress measurements by the crystal curvature technique and structural investigations on different nanoscale systems. It is shown that stress measurements offer highly sensitive and accurate data which identify even subtle structural changes in the sub-monolayer coverage regime. We discuss the unique potential of stress measurements to complement structural investigations of atomic layers and at surfaces. Our examples reveal that stress measurements enhance, support and clarify the interpretation of quantitative structural data. The role of surface stress and film stress for structural transitions in epitaxial growth, surfactant-mediated growth, surface reconstruction and adsorbate-induced spin reorientation transitions in monolayers is discussed.