  The MUonE experiment aims at an independent and very precise determination of
the leading hadronic contribution to the muon magnetic moment, based on an
alternative method, complementary to the existing ones. This can be achieved by
measuring with unprecedented precision the shape of the differential cross
section of $\mu e$ elastic scattering, using the intense muon beam available at
CERN, with energy of 150 GeV, off atomic electrons of a light target. The
status of the project is presented, with recent results in preparation for the
test run scheduled in 2021 with a reduced detector.
