  In this talk an analysis of the rare exclusive $B$ decays $B\to K\nu\bar\nu$
and $B\to K^{*}\nu\bar\nu$ within and beyond the Standard Model is presented.
Combining new form factor determinations from lattice QCD with light-cone sum
rule results and including complete two-loop electroweak corrections to the SM
Wilson coefficient, precise Standard Model predictions will be given. Beyond
the SM, we make use of an effective theory with dimension-six operators
invariant under the SM gauge symmetries to relate NP effects in $b\to
s\bar\nu\nu$ transitions to $b\to s\ell^+\ell^-$ transitions and use the wealth
of experimental data on $B\to K^{(*)}\ell^+\ell^-$ and related modes to
constrain NP effects in $B\to K^{(*)}\nu\bar\nu$. We then consider leptoquark
models as a showcase for models where in principle large effects are possible.
