This thesis details four different studies of accretion and emission processes around the Galactic Center Sgr A*. We are studying Sgr A* in particular because it is the closest supermassive black hole and therefore we have incomparable observational data to test our theories and predictions. However, as explained in the introduction, the physics is certainly similar to that around other supermassive black holes at the center of many other galaxies, and comparable as well to the accretion and emission processes around hundreds of millions of smaller mass black holes that are present in our Milky Way. It is interesting to understand what is happening around compact objects like black holes, because they are at the origin of the most energetic phenomena in the universe (such as jet launching) and therefore have an important role in its evolution. Moreover physical conditions around a black hole are extremely different to anything we can see and reproduce on Earth; Sgr A* is thus an excellent laboratory to test the limits of our understanding of compact objects and phenomena surrounding them.