At the center of our Milky Way Galaxy lives a compact massive object called Sagittarius A* (Sgr A*) which is believed to be a black hole. Its mass, as inferred from the orbits of gravitationally bound stars as well as from direct images obtained by the Event Horizon Telescope, is 4 million solar masses. Gas accreting gravitationally on Sgr A* is in an unusual regime of plasma physics whose properties are the focus of the accompanying joint PGI/PCTS Workshop. While it seems highly likely that Sgr A* is indeed a black hole, with an event horizon, it would be wise to ask if alternative models are also viable. The talk will describe efforts to eliminate some of the alternatives.