Sgr A*: The optimal testbed of strong-field gravity

The black hole in the center of the Milky Way has been observed and modeled intensely during the last decades. It is also the prime target of a number of new experiments that aim to zoom into the vicinity of its horizon and reveal the inner working of its spacetime. In this review we discuss our current understanding of the gravitational field of Sgr A* and the prospects of testing the Kerr nature of its spacetime via imaging, astrometric, and timing observations.