  In molecular dynamics, several algorithms have been designed over the past
few years to accelerate the exit event from a metastable region of the
configuration space. Some of them are based on the fact that the exit event
from a metastable region is well approximated by a Markov jump process. In this
work, we present recent results on the exit event from a metastable region for
the overdamped Langevin dynamics obtained in [17, 18, 49]. These results aim in
particular at justifying the use of a Markov jump process parametrized by the
Eyring-Kramers law to model the exit event from a metastable region.
