The DART spacecraft is planned to impact the secondary of the binary asteroid (65803) Didymos in 2022, to assess deflection strategies for planetary defense. The impact will create a crater and release asteroidal material, some of which will escape the Didymos system. Because the closest point of approach of Didymos to Earth's orbit is only 6 million km (about 16 times the Earth-Moon distance), some ejected material will make its way sooner or later to our planet, and the observation of these particles as meteors would increase the scientific payout of the DART mission. The DART project may also represent the first human-generated meteoroids to reach Earth, and a test case for human activity on asteroids and its eventual contribution to the meteoroid environment and spacecraft impact risk. This study examines the amount and timing of the delivery of meteoroids from Didymos to near-Earth space.This study finds that very little DART-ejected material will reach our planet, and most of that only after thousands of years. But some material ejected at the highest velocities could be delivered to Earth-crossing trajectories almost immediately, though at very low fluxes. Timing and radiant directions for material reaching Earth are calculated, though the detection of substantial numbers would indicate more abundant and/or faster ejecta than is expected.The DART impact will create a new meteoroid stream, though probably not a very dense one. However, larger, more capable asteroid impactors could create meteoroid streams in which the particle flux exceeds that naturally occurring in the Solar System, with implications for spacecraft safety.