In this talk I will discuss the recently further strengthened hints for new physics in semileptonic B-meson decays, focusing on the 'clean' ratios of branching fractions RK and RK∗ and examining to which pattern of new effects they point to. I will focus in particular on the hardly considered, yet fully viable, option of new physics in the right-handed electron sector and demonstrate how a recently proposed framework of leptons in composite Higgs setups naturally solves both the RK and RK∗ anomalies via a peculiar structure of new physics effects, predicted by minimality of the model and the scale of neutrino masses. I will also consider further observables, such as B(Bs→μ+μ−), ΔMBs, and angular observables in B→K∗μ+μ− decays, to arrive at a comprehensive picture of the model concerning (semileptonic) B decays.