The existence of black holes has been predicted for a long time, even before general relativity was sketched by Albert Einstein. Their extreme compactness makes them difficult to explore on spatial scales close to the event horizon. Sagittarius A*, at the center of the Galaxy, is the black hole with the largest angular size. A collaboration of European astronomers has built the GRAVITY instrument for the Very Large Telescope Interferometer of ESO to test the black hole nature of Sgr A* thanks to observations in the infrared at unprecedented spatial scales. General relativity can consequently also be tested at these scales in an extreme regime of gravity. I will present the results we have obtained with the star S2, the closest star known to Sgr A*. I will also present the first resultst on infrared flares occuring near the event horizon. I will conclude on the prommising prospects of GRAVITY.