Measurements of electroweak penguin and lepton-flavour violating $B$ decays to final states with missing energy at Belle and Belle II

The Belle and Belle II experiments have collected a 1.2 ab$^{-1}$ sample of $e^+e^-\to B\bar B$ collisions at a centre-of-mass energy corresponding to the $\Upsilon(4S)$ resonance. These data, with low particle multiplicity and constrained initial state kinematics, are an ideal environment to search for rare electroweak penguin $B$ decays and lepton-flavour-violating $B$ decays to final states with missing energy from neutrinos. Results from $b\to s \nu\bar\nu$ processes and their interpretation are presented. In addition, we present searches for the processes $B\to K^{*0}\tau^+\tau^-$. Finally, we present our search for the lepton-flavour violating decay $B^0\to K^{*0}\tau^\pm\ell^{\pm}$, and $B^0\to K^{0}_S\tau^\pm\ell^{\pm}$ where $\ell$ is an electron or muon.