In 1987, Gromov gave several ways to convert any cell complex K into a nonpositvely curved cell complex H(K). He claimed that the metric on these new cell complexes could be made strictly negatively curved; however, this was later disproved. In 1995 Charney and Davis gave a modified hyperbolization technique which did produce negatively curved cell complexes. I will talk about both the Gromov and Charney-Davis versions of this result, and then discuss some applications. Speaker(s): Kevin Schreve (University of Michigan)