Recently, Belle-II reported on the first measurement of $\mathcal{B}(B\to K \nu \nu)$ and found that its value is about 3σ above the one predicted in the Standard Model (SM). We study this and similar exclusive processes based on $b \to s \nu \nu$ by using effective field theory (EFT) in order to understand if such a deviation can be attributed to some heavy mediator beyond the SM. We point out the correlations with other observables that can be measured in the near future, $\mathcal{B}(B\to K^\ast \nu \nu)$ in particular, and show how the similar decays to charged leptons can help constraining the allowed parameter space when working within the SMEFT approach. We also comment on the possibility of having a light mediator or a heavy neutrino species in the final state, such as a sterile neutrino which is often evoked to accommodate a few anomalies present in neutrino oscillation experiments.
