  The East model is a particular one dimensional interacting particle system in
which certain transitions are forbidden according to some constraints depending
on the configuration of the system. As such it has received particular
attention in the physics literature as a special case of a more general class
of systems referred to as kinetically constrained models, which play a key role
in explaining some features of the dynamics of glasses. In this paper we give
an extensive overview of recent rigorous results concerning the equilibrium and
non-equilibrium dynamics of the East model together with some new improvements.
