Charged Higgs: Interpretation of $B$-physics results

In these proceedings we review the impact of additional Higgs bosons on $B$ physics observables. For this purpose, we consider first the 2HDM of type II which respects natural flavour conservation. Afterwards, we study a 2HDM with generic flavour structure (of type III). While constraints from $B_{s,d}\to\mu^+\mu^+$ impose stringent bounds on non-minimal flavour violation in the down sector, $b\to s,d\gamma$ can also constrain flavour violation in the up sector. Despite these stringent constraints and the recent CMS bounds from $A^0\to\tau^+\tau^-$ it is shown that still large effects in tauonic $B$ decays are possible, such that the BABAR measurements of these decays can be explained. The matching of the Yukawa sector of the MSSM on the 2HDM is discussed.