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$B$ Decays and Lepton Flavour (Universality) Violation

LHCb found hints for physics beyond the standard model in $B\to K^*μ^+μ^-$, $B\to K^*μ^+μ^-/B\to K^*e^+e^-$ and $B_s\toϕμ^+μ^-$. In addition, the BABAR results for $B\to D^{(*)}τν$ and the CMS excess in $h\toτ^\pmμ^\mp$ also point towards lepton flavour (universality) violating new physics. While $B\to D^{(*)}τν$ and $h\toτ^\pmμ^\mp$ can be naturally explained by an extended Higgs sector, the probably most promising explanation for the $b\to sμμ$ anomalies is a $Z'$ boson. Furthermore, combining a 2HDM with a gauged $L_μ-L_τ$ symmetry allows for explaining the $b\to sμ^+μ^-$ anomalies and $h\toτ^\pmμ^\mp$ simultaneously, with interesting correlations to $τ\to3μ$. In the light of these deviations from the SM we also discuss the possibilities of observing lepton flavour violating $B$ decays (e.g. $B\to K^{(*)}τ^\pmμ^\mp$ and $B_s\toτ^\pmμ^\mp$) in $Z^\prime$ models.