  We study the class of monotone, two-state, deterministic cellular automata,
in which sites are activated (or 'infected') by certain configurations of
nearby infected sites. These models have close connections to statistical
physics, and several specific examples have been extensively studied in recent
years by both mathematicians and physicists. This general setting was first
studied only recently, however, by Bollob\'as, Smith and Uzzell, who showed
that the family of all such 'bootstrap percolation' models on $\mathbb{Z}^2$
can be naturally partitioned into three classes, which they termed subcritical,
critical and supercritical.
  In this paper we determine the order of the threshold for percolation
(complete occupation) for every critical bootstrap percolation model in two
dimensions. This 'universality' theorem includes as special cases results of
Aizenman and Lebowitz, Gravner and Griffeath, Mountford, and van Enter and
Hulshof, significantly strengthens bounds of Bollob\'as, Smith and Uzzell, and
complements recent work of Balister, Bollob\'as, Przykucki and Smith on
subcritical models.
