  The Event Horizon Telescope is a millimeter VLBI array that aims to take the
first pictures of the black holes in the center of the Milky Way and of the M87
galaxy, with horizon scale resolution. Measurements of the shape and size of
the shadows cast by the black holes on the surrounding emission can test the
cosmic censorship conjecture and the no-hair theorem and may find evidence for
classical effects of the quantum structure of black holes. Observations of
coherent structures in the accretion flows may lead to accurate measurements of
the spins of the black holes and of other properties of their spacetimes. For
Sgr A*, the black hole in the center of the Milky Way, measurements of the
precession of stellar orbits and timing monitoring of orbiting pulsars offer
complementary avenues to the gravitational tests with the Event Horizon
Telescope.
