This is an announcement for the paper "Embedding into Banach spaces with finite dimensional decompositions" by E. Odell and Th. Schlumprecht. Abstract: This paper deals with the following types of problems: Assume a Banach space $X$ has some property (P). Can it be embedded into some Banach space $Z$ with a finite dimensional decomposition having property (P), or more generally, having a property related to (P)? Secondly, given a class of Banach spaces, does there exist a Banach space in this class, or in a closely related one, which is universal for this class? Archive classification: Functional Analysis Mathematics Subject Classification: 46B03; 46B20 Remarks: 26 pages The source file(s), os-embedding-final.tex: 109527 bytes, is(are) stored in gzipped form as 0701324.gz with size 33kb. The corresponding postcript file has gzipped size 182kb. 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/0701324 or http://arXiv.org/abs/math.FA/0701324 or by email in unzipped form by transmitting an empty message with subject line uget 0701324 or in gzipped form by using subject line get 0701324 to: math@arXiv.org.