  Kinetically constrained models (KCMs) are interacting particle systems on
$Z^d$ with a continuous-time constrained Glauber dynamics, which were
introduced by physicists to model the liquid-glass transition. One of the most
well-known KCMs is the one-dimensional East model. Its generalization to higher
dimension, the d-dimensional East model, is much less understood. Prior to this
paper, convergence to equilibrium in the d-dimensional East model was proven to
be at least stretched exponential, by Chleboun, Faggionato and Martinelli in
2015. We show that the d-dimensional East model exhibits exponential
convergence to equilibrium in all settings for which convergence is possible.
