A massive black hole resides in the center of most, perhaps all galaxies. The one in the center of our home galaxy, the Milky Way, provides a uniquely accessible laboratory for studying in detail the connections and interactions between a massive black hole and the stellar system in which it grows; for investigating the effects of extreme density, velocity and tidal fields on stars; and for using stars to probe the central dark mass and to probe post-Newtonian gravity in the weak- and strong-field limits. Recent results, open questions and future prospects are reviewed in the wider context of the theoretical framework and physical processes that underlie them.