The simple symmetric exclusion process on Z models the dynamics of particles with strong local interaction induced by an exclusion rule: each attempts the motion of a nearest-neighbor symmetric random walk, but jumps to occupied sites are suppressed. While this process has been studied extensively over the past several decades, not much has been known rigorously about the behavior of extremal particles when the system is out of equilibrium. We consider a `step’ initial condition in which infinitely many particles lie below a maximal one. As time tends to infinity, the system becomes indistinguishable from one without particle interaction, in the sense that the point process of particle positions, appropriately scaled, converges in distribution to a Poisson process on the real line with intensity exp(-x)dx. Correspondingly, the position of the maximal particle converges to the Gumbel distribution exp(-exp(-x)), which answers a question left open by Arratia (1983). I will discuss several properties of the symmetric exclusion process that lead to this result, including negative association, self-duality, and the so-called `stirring’ construction, as well as extensions to higher dimensions and to dynamics that allow more than one particle per site. The talk is based on joint work with Sunder Sethuraman and Adrián González Casanova.