Using Lumen gentium as a focus, what can we say about the unfinished business of renewal? How does it work, and how must we read Lumen gentium in order to grasp “what remains to be done”? We consider four issues, each of them in dialogue with one of four theologians who reached their 60th birthday in 1964, the year Lumen gentium was completed. Bernard Lonergan helps us come to terms with the historically conditioned nature of Lumen gentium itself. Karl Rahner points the way towards a better grasp of Lumen gentium's discussion of the place of other religions in the economy of salvation. John Courtney Murray's influence on the Council fathers is a case study in the importance of the local church. And Yves Congar's willingness to rethink his own positions testifies to the importance of not making Lumen gentium into unchanging truth. Overall, the unfinished business of the document on the Church is to learn to treat it, in Lonergan's words, as “not premisses but data.”