Depending on the assumptions on the power corrections to the exclusive b → sℓ+ℓ- decays, the latest data of the LHCb Collaboration - based on the 3 fb-1 data set and on two different experimental analysis methods - still shows some tensions with the Standard Model predictions. We present a detailed analysis of the theoretical inputs and various global fits to all the available b → sℓ+ℓ- data. This constitutes the first global analysis of the new data of the LHCb Collaboration based on the hypothesis that these tensions can be at least partially explained by new physics contributions. In our model-independent analysis we present one-, two-, four-, and also five-dimensional global fits in the space of Wilson coefficients to all available b → sℓ+ℓ- data. We also compare the two different experimental LHCb analyses of the angular observables in B →K⁎μ+μ-. We explicitly analyse the dependence of our results on the assumptions about power corrections, but also on the errors present in the form factor calculations. Moreover, based on our new global fits we present predictions for ratios of observables which may show a sign of lepton non-universality. Their measurements would crosscheck the LHCb result on the ratio RK = BR (B+ →K+μ+μ-) / BR (B+ →K+e+e-) in the low-q2 region which deviates from the SM prediction by 2.6σ.