  I discuss the quantum dynamics of strongly disordered quantum systems with
critically long range interactions, decaying as $1/r^{2d}$ in $d$ spatial
dimensions. I argue that, contrary to expectations, localization in such
systems is stable at low orders in perturbation theory, giving rise to an
unusual `critically many body localized regime.' I discuss the phenomenology of
this critical MBL regime, which includes distinctive signatures in
entanglement, charge statistics, noise, and transport. Experimentally, such a
critically localized regime can be realized in three dimensional systems with
Van der Waals interactions, such as Rydberg atoms, and in one dimensional
systems with $1/r^2$ interactions, such as trapped ions. I estimate timescales
on which high order perturbative and non-perturbative (avalanche) phenomena may
destabilize this critically MBL regime, and conclude that the avalanche sets
the limiting timescale, in the limit of strong disorder / weak interactions.
