Sweden's Rolf Schock Prize, awarded to Sol Feferman on May 15, 2003, was identified as being "for his works on the arithmetization of metamathematics, transfinite progressions of theories and predicativity." This last area, predicativity, is the subject of this talk. I will provide a brief history, describing some of Sol's work in this area, and then I will talk about my own work (some of it together with Jeremy Avigad) using model-theoretic methods to give a proof-theoretic analysis of predicative theories.