The coupling of the electroweak gauge bosons of the Standard Model (SM) of particle physics to leptons is flavour universal. Experimental tests of this principle are highly sensitive to New Physics particles which couple differently among the leptonic families. A violation of lepton flavour universality, together with the flavour anomalies that have been observed, could imply the existence of lepton-flavour violating $b$-hadron decays. Recent results from the LHCb experiment on lepton flavour universality and lepton flavour violation are discussed in this talk.