  We present a systematic global analysis of dineutrino modes $b \to q \,\nu
\bar \nu$, $q=d,s$, and charged dilepton $b \to q \,\ell^+ \ell^-$ transitions.
We derive improved or even entirely new limits on dineutrino branching ratios
including decays $B^0 \to (K^0 , X_s)\, \nu \bar \nu$, $B_s \to \phi \,\nu \bar
\nu$ and $B^0 \to (\pi^0, \rho^0)\, \nu \bar \nu$ from dineutrino modes which
presently are best constrained: $B^+ \to (K^+,\pi^+, \rho^+) \,\nu \bar \nu$
and $B^0 \to K^{*0} \,\nu \bar \nu$. 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
$e \tau$ and $\tau \tau$ final states, as well as for $\mu \tau$ ones in $b \to
s$ processes. The method also allows to put novel constraints on semileptonic
four-fermion operators with top quarks. Implications for ditau modes $b \to s
\, \tau^+ \tau^-$ and $b \to d \, \tau^+ \tau^-$ are worked out. 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 $b \to s \,\mu^+ \mu^-, \,s \gamma$ transitions we find that lepton
universality predicts the ratio of the $B^0 \to K^{*0} \,\nu \bar \nu$ to $B^0
\to K^0 \,\nu \bar \nu$ ($B^+ \to K^+ \,\nu \bar \nu$) branching fractions to
be within 1.7 to 2.6 (1.6 to 2.4) at $1\,\sigma$, 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 $B^0 \to
\mu^+ \mu^-$, $B^0_s\to \bar{K}^{\ast 0}\,\mu^+\mu^-$ and $ B^+ \to \pi^+\,
\mu^+ \mu^-$ data we obtain an analogous relation for $|\Delta b|=|\Delta d|=1$
transitions.
