The Galactic Center 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, our Galactic Center offers a unique laboratory to test gravity. In this review we provide a general overview of the history of observations of the GC, focusing in particular on the smallest-observable scales, and on the impact that such observations have on our understanding of the underlying theory of gravity in the surrounding of a massive compact object.