Rare decays of beauty, charm and strange hadrons, which proceed via flavour changing neutral current transitions, provide a powerful test of the Standard Model (SM). In the SM, these decays are forbidden at tree level and therefore are strongly suppressed. For example, b → (s,d) l+l- processes give access to several observables, such as differential branching fractions and angular variables, where effects of new physics could be observed. Hints of lepton flavour non-universality have been seen when comparing the B0→K∗0μ+μ− and B0→K∗0e+e− decay rates, as well as those of B+→K+μ+μ- and B+→K+e+e-, with the so-called RK* and RK ratios. In a related sector, which involves charged-current tree-level transitions, the world average for the ratios R(D(∗)) = BF(B0→D(∗)τν)/BF(B0→D(∗)μν) deviates from the very precise prediction of the SM by about four standard deviations, yielding another intriguing hint of potential new physics effects in the flavour sector. I will review the present status of new physics searches in this area, discussing recent, relevant measurements at LHCb. In closing I will also discuss some further highlights in other prominent areas of the LHCb research programme.
