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Charm physics plays a major role in the physics program of LHCb and offers a unique opportunity to search for physics beyond the standard model in the up-type quark sector. Thanks to the enormous charm production rate at the LHC, LHCb has collected the world's largest sample of charmed hadrons. This sample is used to measure decay processes which are sensitive to quantum-loop corrections, such as $D^0 -\overline{D}^0$ mixing, $C\!P$ asymmetries and properties of rare decays. This talk gives an overview of the charm physics program at LHCb, recent results and plans for the future.