The Galactic Center as a laboratory for theories of gravity and dark matter

The Galactic Center (GC) of the Milky Way, thanks to its proximity, allows to perform astronomical observations that investigate physical phenomena at the edge of astrophysics and fundamental physics. As such, it offers a unique laboratory to probe gravity, where one can not only test the basic predictions of general relativity (GR), but is also able to falsify theories that, over time, have been proposed to modify or extend GR; to test different paradigms of dark matter; and to place constraints on putative models that have been formulated as alternatives to the standard black hole paradigm in GR. In this review we provide a general overview of the history of observations of the GC, emphasizing the importance, in particular on the smallest-observable scales, that they had in opening a new avenue to improve our understanding of the underlying theory of gravity in the surrounding of a supermassive compact object.