A fraction of the dark matter in the solar neighborhood might be composed of non-galactic particles with speeds larger than the escape velocity of the Milky Way. The non-galactic dark matter flux would enhance the sensitivity of direct detection experiments, due to the larger momentum transfer to the target. In this contribution, we first summarize our current knowledge of the dark matter distribution outside the Milky Way, we then review the modelling of the non-galactic dark matter flux at the Solar System, and we finally assess its impact on sub-GeV direct detection experiments searching for both nuclear and electron recoils.