Flavor Anomalies in Heavy Quark Decays

Recent measurements of $b$-hadron decays show a pattern of consistent tensions with the respective Standard Model (SM) predictions. These tensions appear both in the sector of rare flavour-changing neutral currents and in tree-level semileptonic $b$-hadron decays. Flavour-changing neutral-current decays are loop-suppressed in the SM and are thus very susceptible to contributions from new heavy particles and/or new interactions beyond the SM. In rare semileptonic decays tensions are observed in measurements of branching fractions and angular observables, as well as in lepton flavour universality tests. Lepton flavour universality is also tested by comparing tree-level $b\to c\ell^-\bar{\nu}_\tau$ processes involving third generation leptons $\ell=\tau$ to semileptonic decays with light leptons $\ell=e,\mu$ in the final state. These tests also show tensions between measurements and the SM prediction. Taken together, these tensions constitute the so-called flavour anomalies in $b$-hadron decays, and could be first signs of New Physics (NP) beyond the SM, if established beyond any reasonable doubt. This article reviews both the current experimental status of the flavour anomalies and developments for the relevant theoretical predictions. The review concludes with a discussion of future prospects for the field.