  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, it offers a unique
laboratory to probe gravity, where one can not only test the basic predictions
of General Relativity, but is also able to falsify theories that, over time,
have been proposed to modify or extend General Relativity; 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 General
Relativity. In this review we provide a general overview of the history of
observations of the Galactic Center, 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.
