Constraints on New Physics from $B$ mesons

These proceedings review the status of New Physics contributions to flavour violating $B$ decays. The anomalies in charged and neutral current $B$ decays related to lepton flavour universality violation have received a substantial amount of attention over the past years, and we discuss the current status in light of the new data presented earlier this year. We also recall a tension in the neutral $B$ meson mixing observables $\Delta M_d$ and $\Delta M_s$ and in particular their ratio, when compared with their SM predictions obtained using tree-level determinations of the CKM matrix and the recent lattice QCD results for the relevant hadronic matrix elements. Last but not least, we advocate kaon physics as a unique probe of very high energy scales and briefly discuss the current status of $\varepsilon'/\varepsilon$ and $K\to\pi\nu\bar\nu$.Comment: 15 pages, 4 figures. v2: typos corrected and reference added. Proceedings of the XXIX International Symposium on Lepton Photon Interactions at High Energies - LeptonPhoton2019, 5-10 August 2019, Toronto, Canad