Black-hole astrophysics has matured to the point that, in the very near future, various observatories will routinely detect strong-field gravitational effects. In this talk, I assess in a quantitave way the prospect of testing strong-field general relativity using observations of supermassive black holes. I show that the external spacetimes of supermassive black holes predicted by a wide variety of alternative gravity theories, including scalar-tensor, higher-order, and large-extra-dimension theories, are practically indistinguishable. This argues that it is virtually impossible to use observations of supermassive black holes to test alternative gravity theories, unless matter outside the black-hole horizon alters significantly the outcome of gravitational experiments. On the other hand, the robustness of the predicted external spacetimes allow us to test the validity of some of the most basic assumptions of gravitational physics.