Abstract:We present an analysis of the rare exclusive B decays B → Kνν and B → K * νν within the Standard Model (SM), in a model-independent manner, and in a number of new physics (NP) models. 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, we obtain the SM predictions BR(B + → K + νν) = (4.0 ± 0.5) × 10 −6 and BR(B 0 → K * 0 νν) = (9.2 ± 1.0) × 10 −6 , more precise and more robust than previous estimates. 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 → sνν transitions to b → s + − transitions and use the wealth of experimental data on B → K ( * ) + − and related modes to constrain NP effects in B → K ( * ) νν. We then consider several specific NP models, including Z models, the MSSM, models with partial compositeness, and leptoquark models, demonstrating that the correlations between b → sνν observables among themselves and with B s → µ + µ − and b → s + − transitions offer powerful tests of NP with new right-handed couplings and non-MFV interactions.