While the crucial role of intrinsically disordered proteins (IDPs) in the cell cycle is now recognized, deciphering their molecular mode of action at the structural level still remains highly challenging and requires a combination of many biophysical approaches. Among them, small angle X-ray scattering (SAXS) has been extremely successful in the last decade and has become an indispensable technique for addressing many of the fundamental questions regarding the activities of IDPs. After introducing some experimental issues specific to IDPs and in relation to the latest technical developments, this article presents the interest of the theory of polymer physics to evaluate the flexibility of fully disordered proteins. The different strategies to obtain 3-dimensional models of IDPs, free in solution and associated in a complex, are then reviewed. Indeed, recent computational advances have made it possible to readily extract maximum information from the scattering curve with a special emphasis on highly flexible systems, such as multidomain proteins and IDPs. Furthermore, integrated computational approaches now enable the generation of ensembles of conformers to translate the unique flexible characteristics of IDPs by taking into consideration the constraints of more and more various complementary experiment. In particular, a combination of SAXS with high-resolution techniques, such as x-ray crystallography and NMR, allows us to provide reliable models and to gain unique structural insights about the protein over multiple structural scales. The latest neutron scattering experiments also promise new advances in the study of the conformational changes of macromolecules involving more complex systems.