$B$ Decays and Lepton Flavour (Universality) Violation

LHCb found hints for physics beyond the standard model in $B\to K^*\mu^+\mu^-$, $B\to K^*\mu^+\mu^-/B\to K^*e^+e^-$ and $B_s\to\phi\mu^+\mu^-$. In addition, the BABAR results for $B\to D^{(*)}\tau\nu$ and the CMS excess in $h\to\tau^\pm\mu^\mp$ also point towards lepton flavour (universality) violating new physics. While $B\to D^{(*)}\tau\nu$ and $h\to\tau^\pm\mu^\mp$ can be naturally explained by an extended Higgs sector, the probably most promising explanation for the $b\to s\mu\mu$ anomalies is a $Z'$ boson. Furthermore, combining a 2HDM with a gauged $L_\mu-L_\tau$ symmetry allows for explaining the $b\to s\mu^+\mu^-$ anomalies and $h\to\tau^\pm\mu^\mp$ simultaneously, with interesting correlations to $\tau\to3\mu$. In the light of these deviations from the SM we also discuss the possibilities of observing lepton flavour violating $B$ decays (e.g. $B\to K^{(*)}\tau^\pm\mu^\mp$ and $B_s\to\tau^\pm\mu^\mp$) in $Z^\prime$ models.