A project of Astronomy over the last 50 years has been to measure the positions and velocities of gas and stars in the center of our own Milky Way galaxy with increasingly high precision. I will review the observations of orbiting stars around the central black hole, which won a share of the Nobel prize in Physics this year. It has now become possible to resolve spatial scales comparable to the event horizon itself using long baseline interferometry at submillimeter and near-infrared wavelengths. I will discuss the detection of relativistic effects in a stellar orbit, and of the black hole "shadow" in an image of synchrotron radiation from magnetized gas near its event horizon. I will outline the challenge of pushing towards tests aimed at determining whether black holes in the Universe are those predicted by General Relativity.