Recent data on b→sℓ+ℓ− transitions (ℓ=e,μ) exhibit a very interesting pattern of deviations from Standard Model expectations. I will recall the current situation of these anomalies in the B→K∗μ+μ− decay, as well as for other outstanding b→sℓ+ℓ− observables, in particular those indicating a violation of lepton-flavour universality (LFU). I will show how a model-independent global fit of b→sℓ+ℓ− observables favours several New Physics scenarios with high significances, with a remarkable degree of consistency between LFU-violating ratios and b→sμ+μ− observables. I will discuss alternative Standard Model explanations for these anomalies critically, relating them to issues in the corresponding theoretical computation. Finally, I will introduce new LFU-violating observables of interest for LHCb and Belle II which are able to shed further light on the cause of these anomalies.