In the centre of our Galaxy lies Sgr A*, a 3.5 × 10 solar mass black hole, immersed in a star cluster with dozens of massive stars. The very low luminosity of Sgr A*, and the presence of young stars in the close proximity of a supermassive black hole, make the Galactic centre a very interesting region on its own. Moreover, its proximity allows the study of the physics of galactic nuclei with a level of detail unattainable in any other system. In this thesis, we first show that the interaction of massive stars with an accretion disc would appear as strongly variable emission in the near infra-red. Since observations have not shown this variability, we strongly constrain the current existence of such a disc in the Galactic centre. We argue however that a massive gaseous disc existed around Sgr A* only a few million years ago. The evidence for this idea comes from the presence of young massive stars in two stellar discs. We estimate the properties of the gaseous disc that gave rise to the massive stars, and we analyse the stellar orbits to constrain this scenario. A related but separate topic presented here is the role of the stellar winds expelled by the same stars in feeding Sgr A* and shaping its immediate gaseous environment. We find that a fraction of these stellar winds form cold clumps that coexist with the X-ray emitting gas, forming a two-phase medium. Only a small fraction of the gas is captured by Sgr A*, with an accretion rate strongly variable on time-scales of hundreds of years. This variability suggests that the time-averaged energy output of Sgr A* may be much larger than what is currently observed.