The MUonE experiment aims to measure the differential cross section of the $\mu \ e$ elastic scattering using the CERN SPS muon beam with mean energy of 160 GeV onto atomic electrons of a low-Z target. Thanks to the intense M2 beam with in-spill intensity of $5\times10^7$ muons/s, a precise measurement of the scattering angles allows to extract the running QED coupling, and by a novel approach the leading hadronic contribution to the muon anomalous magnetic moment. This determination will be completely independent from the usual data-driven method, based on measurements of the R-ratio in $e^+e^-$ annihilations, and could clarify the discrepancy between these results and the theory-based estimates from recent lattice QCD calculations.
\newline The MUonE challenge resides in the control of theoretical and experimental uncertainties to an unprecedented level of precision for a scattering experiment. A pilot run was held this summer, operating for the first time two tracking stations and a prototype electromagnetic calorimeter connected to a triggerless readout system. The status and plans of the experiment will be presented.