  Recent experimental results on angular observables in the rare decay $B\to
K^*\mu^+\mu^-$ show significant deviations from Standard Model predictions. We
investigate the possibility that these deviations are due to new physics.
Combining all relevant data on $b \to s$ rare decays, we show that a consistent
explanation of most anomalies can be obtained by new physics contributing
simultaneously to the semi-leptonic vector operator $O_9$ and its
chirality-flipped counterpart $O_9'$. A partial explanation is possible with
new physics in $O_9$ or in dipole operators only. We study in detail the
implications for models of new physics, in particular the minimal
supersymmetric standard model, models with partial compositeness and generic
models with flavour-changing $Z^\prime$ bosons. In all considered models,
contributions to $B\to K^*\mu^+\mu^-$ of the preferred size imply a spectrum
close to the TeV scale. We stress that measurements of CP asymmetries in $B\to
K^*\mu^+\mu^-$ could provide valuable information to narrow down possible new
physics explanations.
