Simbol-X is a French-Italian mission, with a participation of German laboratories, for X-ray astronomy in the wide 0.5-80 keV band. Taking advantage of emerging technology in mirror manufacturing and spacecraft formation flying, Simbol-X will push grazing incidence imaging up to ~80 keV, providing an improvement of roughly three orders of magnitude in sensitivity and angular resolution compared to all instruments that have operated so far above 10 keV. This will open a new window in X-ray astronomy, allowing breakthrough studies on black hole physics and census and particle acceleration mechanisms. We describe briefly the main scientific goals of the Simbol-X mission, giving a few examples aimed at highlighting key issues of the Simbol-X design.