In the Standard Model (SM), the rare transitions where a bottom quark decays into a strange quark and a pair of light leptons exhibit a potential sensitivity to physics beyond the SM. In addition, the SM embeds Lepton Flavour Universality (LFU), leading to almost identical probabilities for muon and electron modes. The LHCb collaboration discovered a set of deviations from the SM expectations in decays to muons and also in ratios assessing LFU. Other experiments (Belle, ATLAS, CMS) found consistent measurements, albeit with large error bars. We perform a global fit to all available b -> sl(+)l(-) data (l = e, mu) in a model-independent way allowing for different patterns of New Physics. For the first time, the NP hypothesis is preferred over the SM by 5 sigma in a general case when NP can enter SM-like operators and their chirally-flipped partners. LFU violation is favoured with respect to LFU at the 3-4 sigma level. We discuss the impact of LFU-violating New Physics on the observable P'(5) from B -> K*mu(+)mu(-) and we compare our estimate for long-distance charm contributions with an empirical model recently proposed by a group of LHCb experimentalists. Finally, we discuss NP models able to describe this consistent pattern of deviations.