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Decays of b hadrons provide a powerful probe for new physics effects that may violate the Standard Model's paradigm of Lepton Flavor Universality, whereby the three charged lepton flavors are distinguished only by their differing masses. A definitive observation of a deviation from the predictions of LFU would provide unambiguous evidence of new physics. Recent measurements have shown a series of tantalizing results which, while not individually significant, are deserving of close scrutiny. I will review the methods and results of recent measurements by LHCb in semileptonic b-> c l nu and rare b -> s l l decays which are of interest in this context, and discuss future prospects for the LHCb program in this area.