We present results of global fits of all relevant experimental data on rare
b→s decays. We observe significant tensions between the Standard Model
predictions and the data. After critically reviewing the possible sources of
theoretical uncertainties, we find that within the Standard Model, the tensions
could be explained if there are unaccounted hadronic effects much larger than
our estimates. Assuming hadronic uncertainties are estimated in a sufficiently
conservative way, we discuss the implications of the experimental results on
new physics, both model independently as well as in the context of the minimal
supersymmetric standard model and models with flavour-changing Z′ bosons. We
discuss in detail the violation of lepton flavour universality as hinted by the
current data and make predictions for additional lepton flavour universality
tests that can be performed in the future. We find that the ratio of the
forward-backward asymmetries in B→K∗μ+μ− and B→K∗e+e−
at low dilepton invariant mass is a particularly sensitive probe of lepton
flavour universality and allows to distinguish between different new physics
scenarios that give the best description of the current data.Comment: 49 pages, 12 figures. v4: matches version published in EPJ