We will present some applications of iterated generic ultrapowers to the study of models of cardinality ℵ1 in various abstract elementary classes. The impetus for this work was the still-open question of absoluteness of ℵ1-categoricity for the class of models of a fixed sentence of Lω1,ω. Most of our result apply to the class of analytically presented AEC's,those whose restrictions to countable models are analytic. This is joint work with Baldwin and Shelah.