  We discuss the impact of recent LHCb data on the B -> K* mu+mu- decay for New
Physics searches. We use an optimised set of observables with a limited
sensitivity to hadronic inputs (form factors), leading to a significant
deviation from the Standard Model for the semileptonic operator O9. We
ascertain the robustness of our results with respect to models of power
corrections, charm-loop effects, factorisation approaches, possible effects
from resonance tails at low-recoil, choice of observables and binnings. We
explain some contradictory results obtained for the chirality-flipped operator
O9prime by different analyses by focusing on the sensitivity of observables at
low recoil afflicted by the psi(4160) and possibly other resonances for B+-> K+
mu+mu- and illustrating the need for a finely binned analysis at large recoil
(rather than a wide [1-6] bin). Finally, we present updated results including
experimental correlations in B -> K* mu+ mu- observables, confirming the
deviation seen with respect to the SM hypothesis (4.2 sigma for large-recoil
data, 3.5 sigma for large- and low-recoil data).
