This is an announcement for the paper "A universal reflexive space for the class of uniformly convex Banach spaces" by E. Odell and Th. Schlumprecht. Abstract: We show that there exists a separable reflexive Banach space into which every separable uniformly convex Banach space isomorphically embeds. This solves a problem of J.~Bourgain. We also give intrinsic characterizations of separable reflexive Banach spaces which embed into a reflexive space with a block $q$-Hilbertian and/or a block $p$-Besselian finite dimensional decomposition. Archive classification: Functional Analysis Mathematics Subject Classification: 46B03; secondary 46B20 Remarks: 13 pages, amslatex The source file(s), os-universal2-archive.tex: 45823 bytes, is(are) stored in gzipped form as 0507509.gz with size 14kb. The corresponding postcript file has gzipped size 78kb. Submitted from: combs@mail.ma.utexas.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0507509 or http://arXiv.org/abs/math.FA/0507509 or by email in unzipped form by transmitting an empty message with subject line uget 0507509 or in gzipped form by using subject line get 0507509 to: math@arXiv.org.