High-precision measurements of flavour-changing processes are sensitive to the virtual effects of particles at energies beyond the reach of current colliders; thus, any New-Physics addressing the hierarchy problem of the electroweak scale must have a non trivial structure in flavour space to avoid all the stringent flavour constraints. In fact, although no new heavy particles have been identified in the high-energy frontier yet, there are tantalizing tensions with the SM in B-meson decays measured at the LHCb and B factories. The first type of anomalies appear in observables of the FCNC rare b→s ll decays, like in the angular distributions of B→K*μ μ, or in the ratio RK = Γ(B→K μ μ) / Γ(B→K e e) . These are currently in 4σ tension with the SM, putatively corresponding to the tree-level exchange of a neutral particle with mass Λ ~ 10 TeV selectively coupling to muons. The second type of anomalies appear in the CC b→ c τ ν transitions which have been measured through 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 and coupled selectively to τ leptons.
In this talk I will review these decays, discussing the extent up to which the SM predictions are understood and the type of new physics one would need to explain the tensions with the SM. I will also discuss experimental and theoretical prospects to clarify the nature of these anomalies in the near future.