Recent developments in b-quark physics

b-quark physics provides a well-established window to explore the phenomena related to quark flavors as incorporated
in the Standard Model of particle physics and theories beyond. The recent experimental accuracy in B-hadron decays allows for stronger precision tests of the Standard Model (SM) and has revealed some tensions with SM predictions. We review the current status of the determination of the quark mixing elements V_cb and V_ub and the tensions in charged-current transitions and rare decays that indicate an intriguing violation of lepton-flavour universality in these decays.