High velocity stars are unique tools to probe our Milky Way. They travel through the Galaxy, being observed far away from their birthplace, and they give us insights into some of the most extreme phenomena in the local Universe, including supernova explosions and close interactions with a supermassive black hole. The combination of Gaia DR2 radial velocities with the more precise and accurate astrometry provided by Gaia EDR3 makes the best data set available to search for the fastest nearby stars in our Galaxy, with precise full phase space information for ~7 million stars in the Milky Way. In this talk I will present the velocity and spatial distribution of these stars. I will then focus on the fastest sources, presenting a clean subset of stars with a high probability of being unbound from the Galaxy. I will discuss their orbits, their possible origin and the mechanisms responsible for their acceleration.