High-precision measurements of flavor-transitions are sensitive to the virtual effects of particles at energies beyond the reach of current colliders. In fact, although no new heavy particles have been identified yet in the high-energy frontier, there are measurements of semileptonic B-meson decays which are in tension with the SM predictions and suggest the existence of new lepton non-universal interactions. The first type of anomalies appear in the charged-current b→ c τ ν transitions which have been measured through the the ratios RD(*) = Γ(B→D(*) τ ν)/ Γ(B→D(*) l ν), where l is the muon or the electron. The average of the measurements is enhanced with respect to the SM and it would correspond to the tree-level exchange of a charged particle with mass Λ ~ 1 TeV coupled selectively to τ leptons.
The second type appears in observables of the rare b→s ll decays, like the lepton universality ratios RK(*) = Γ(B→K(*) μ μ) / Γ(B→K(*) e e) which are currently in 4σ tension with the SM, putatively corresponding to the tree-level exchange of a neutral particle with mass Λ ~ 10 TeV. In this talk I will review these decays, discussing the extent to which the SM predictions are understood and the type of new physics one would need to explain the data. I will also discuss experimental and theoretical prospects to clarify the nature of these anomalies in the near future.