Rare $b \to s\ell^+\ell^−$ transitions are strongly suppressed in the Standard Model (SM). Leptons from the different families have the same coupling to electroweak bosons in the SM, symmetry that is known as Lepton Flavour Universality. Precise measurements of LFU ratios in $b → s\ell^+\ell^−$ decays provide, then, a very powerful test of the SM. In the same way, any evidence of a Lepton Flavour Violation (LFV) decay would imply a clear sign of New Physics.

These proceedings present a summary of the latest measurements of LFU tests in $B^+ \to K^+\ell^+\ell^-$ and $B^0 \to K^{*0}\ell^+\ell^−$ decays, with $\ell = e, \mu$, and searches for LFV in $B^0 \to K^{*0} \mu^{\pm}e^{\mp}$, $B_s^0 \to \phi\mu^{\pm}e^{\mp}$ and $B^0 \to K^{*0}\tau^{\pm} \mu^{\mp}$ performed at LHCb with the full Run 1 and Run 2 dataset (2011-18, 9 fb−1).