We present a systematic global analysis of dineutrino modes b → q ν ν, q = d, s, and charged dilepton b → q + − transitions. We derive improved or even entirely new limits on dineutrino branching ratios including decays B 0 → (K 0 , Xs) ν ν, Bs → φ ν ν and B 0 → (π 0 , ρ 0 ) ν ν from dineutrino modes which presently are best constrained: B + → (K + , π + , ρ + ) ν ν and B 0 → K * 0 ν ν. Using SMEFT we obtain new flavor constraints from the dineutrino modes, which are stronger than the corresponding ones from charged dilepton rare b-decay or Drell-Yan data, for eτ and τ τ final states, as well as for µτ ones in b → s processes. The method also allows to put novel constraints on semileptonic four-fermion operators with top quarks. Implications for ditau modes b → s τ + τ − and b → d τ + τ − are worked out. Even stronger constraints are obtained in simplified BSM frameworks such as leptoquarks and Z -models. Furthermore, the interplay between dineutrinos and charged dileptons allows for concrete, novel tests of lepton universality in rare B-decays. Performing a global fit to b → s µ + µ − , sγ transitions we find that lepton universality predicts the ratio of the B 0 → K * 0 ν ν to B 0 → K 0 ν ν (B + → K + ν ν) branching fractions to be within 1.7 to 2.6 (1.6 to 2.4) at 1 σ, a region that includes the standard model, and that can be narrowed with improved charged dilepton data. There is sizable room outside this region where universality is broken and that can be probed with the Belle II experiment. Using results of a fit to B 0 → µ + µ − , B 0 s → K * 0 µ + µ − and B + → π + µ + µ − data we obtain an analogous relation for |∆b| = |∆d| = 1 transitions: if lepton universality holds the ratio of the B 0 → ρ 0 ν ν to B 0 → π 0 ν ν (B + → π + ν ν) branching fractions is within 2.5 to 5.7 (1.2 to 2.6) at 1 σ. Putting upper limits on B(Bs → ν ν) at the level of 10 −5 and B(B 0 → ν ν) below 10 −6 would allow to control backgrounds from (pseudo-)scalar operators such as those induced by light right-handed neutrinos.