This paper summarizes the development of a successful project, LAUE, supported by the Italian Space Agency (ASI) and devoted to the development of long focal length (up to 100 m) Laue lenses for hard X--/soft gamma--ray astronomy (80-600 keV). The apparatus is ready and the assembling of a prototype lens petal is ongoing. The great achievement of this project is the use of bent crystals. From measurements obtained on single crystals and from simulations, we have estimated the expected Point Spread Function and thus the sensitivity of a lens made of petals. The expected sensitivity is a few $\times10^{-8}$ photons cm$^{-2}$ s$^{-1}$ keV$^{-1}$. We discuss a number of open astrophysical questions that can settled with such an instrument aboard a free-flying satellite. ; Comment: 17 pages, 18 figures, published in Proceedings of the SPIE, Volume 8861, id. 886106 17 pp. (2013)