Consider the following Markov chain on the set of all possible zero-one labelings of a rooted binary tree of depth L: At each vertex v independently, a proposed new label (equally likely to be 0 or 1) is generated at rate 1. The proposed update is accepted iff either v is a leaf or both children of v are labeled “0”. A natural question is to determine the mixing time of this chain as a function of L. The above is just an example of a general class of chains in which the local update of a spin occurs only in the presence of a special (“facilitating”) configuration at neighboring vertices. Although the i.i.d. Bernoulli distribution remains a reversible stationary measure, the relaxation to equilibrium of these chains can be extremely complex, featuring dynamical phase transitions, metastability, dynamical heterogeneities and universal behavior. I will report on progress on the mixing times for these models.