In this talk we introduce Shelah's approachability ideal I[ω ₂]. We sketch a proof by William Mitchell that it is consistent from a Greatly Mahlo cardinal that I[ω ₂] is the nonstationary ideal on cf(ω ₁). A key idea of the proof is to use side conditions forcing, which we formulate using John Krueger's notion of an adequate set of models. We also discuss the theory of strongly proper forcing posets, another key ingredient of Mitchell's proof. The talk will conclude with an approximation of Mitchell's forcing poset.