10 pages, 6 figures. Published in Comptes Rendus Physique, Volume 8, Issue 1, January 2007, Pages 35-44, "Observation of black holes and extreme gravitational events", Academie des Sciences, Elsevier Science. Available online 2 February 2007The centre of our galaxy hosts the nearest super-massive black hole to the solar system, identified to the compact radio source Sgr A*. High energy experiments have tried in the past to detect the X/gamma-ray emission expected from the accretion of the surrounding material into this super-massive black hole. Only recently however, thanks to the new generation of telescopes, it has been possible to reveal high energy radiation associated with Sgr A* or its close environment. I will review and discuss in p...