Flavour anomalies: a review

Abstract: The concept of lepton flavour universality (LFU), according to which the three lepton families are equivalent except for their masses, is a cornerstone prediction of the Standard Model (SM). LFU can be violated in models beyond the SM by new physics particles that couple preferentially to certain generations of leptons. In the last few years, hints of LFU violation have been observed in both tree-level $b\to c\ell\nu$ and loop-level $b\to s\ell\ell$ transitions. These measurements, combined with the tensions observed in angular observables and branching fractions of rare semileptonic $b$ decays, point to a coherent pattern of anomalies that could soon turn into the first observation of physics beyond the SM. These proceedings review the anomalies seen by the LHC experiments and the $B$ factories, and give an outlook for the near future.