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We report on the deep (100 ksec) XMM-Newton/EPIC observation of the field of the Geminga pulsar. The unprecedented throughput of the instrument allowed to detect two elongated parallel x-ray tails trailing the neutron star. They are aligned with the object's supersonic motion, extend for ∼2', and have a nonthermal spectrum produced by electron-synchrotron emission in the bow shock between the pulsar wind and the surrounding medium. Electron lifetime against synchrotron cooling matches the source transit time over the x-ray fea-tures' length. Such an x-ray detection of a pulsar bow shock allows us to gauge the pulsar electron injection energy and the shock magnetic field while constraining the angle of Geminga's motion and the local matter density. We give also preliminary results on the timing and spectral analysis of the ∼63,000 photons collected from the neutron star.