This lecture is a progress report on a continuing project I am currently working on, namely a critical history of the Galileo affair from 1633 to 1992. The overall project aims to collect, analyze, evaluate, and try to account for the various views about the original trial advanced in the subsequent three and one-half centuries. It plans to relate the story of the aftermath from Descartes' initial reactions to Galileo's condemnation up to his alleged rehabilitation by Pope John Paul II (in 1979-1992). It intends to assess this historical aftermath in terms of such issues as the interaction between science and religion, between conservation and innovation, and between cultural myths and documented facts. It would follow a principled bipartisan approach (avoiding both Galilean or clerical one-sidedness). And it would also follow an approach which is sensitive to both historical and philosophical concerns.