  We discuss the consequences of deviations from the Standard Model observed in
$b\to s\mu^+\mu^-$ transitions for flavour-changing neutral-current processes
involving down-type quarks and neutrinos. We work within an effective field
theory approach respecting the SM gauge symmetry, including right-handed
currents, a flavour structure based on approximate U(2) symmetry, and assuming
only SM-like light neutrinos. We discuss correlations among $B\to
h_s\nu\bar\nu$ ($h_s=K,K^*,X_s$), $K^+\to\pi^+\nu\bar\nu$ and
$K_L\to\pi^0\nu\bar\nu$ branching ratios in the case of linear Minimal Flavour
Violation and in a more general framework.
