  The Belle II experiment at the SuperKEKB energy-asymmetric electron-positron
collider is a substantial upgrade of the B factory facility at the Japanese KEK
laboratory. Belle II collected a sample of $362~\mathrm{fb}^{-1}$ at the
$\Upsilon(4S)$ resonance between 2019 and 2022, with a maximum peak luminosity
of $4.7 \times 10^{34} \mathrm{cm}^{-2}s^{-1}$. Belle II is currently facing a
long shutdown period, required for several upgrades of the detector and the
collider. Data taking will resume at the end of 2023. We report the recent
measurements which involve neutral current transitions in $B$ meson decays. In
particular, we present the current status and future prospects for the
branching fractions measurements of the radiative decays $B\to K^*\gamma$ and
the fully inclusive $B\to X_s\gamma$, the search for $B^+\to K^+\nu\bar \nu$
decays, the measurement of the branching fractions of $B\to J/\psi(\to
\ell\ell)K$ and $B\to K^*\ell\ell$. Finally, we show the perspectives of the
search for $B\to K^{*}\tau\tau$ and the searches of lepton flavor violating
channels $B\to K^{(*)}\ell\ell'$, with $\ell=e, \mu, \tau$.
