Abstract: Bootstrap percolation is a classical model for a dynamical network, in which sites (e.g., people) in a network update their status (e.g., become infected) depending on the status of their local network (e.g., depending on how many of their close contacts are infected). Béla Bollobás introduced a variant of this model, called graph bootstrap percolation, wherein the rule by which sites change status is significantly more complex/realistic. In this talk, we will discuss our recent work with Zsolt Bartha, which locates the critical percolation threshold, at which point it becomes likely that all sites are eventually infected. This solves an open problem of József Balogh, Béla Bollobás and Robert Morris.