This is an announcement for the paper "Recent progress and open questions on the numerical index of Banach spaces" by Vladimir Kadets, Miguel Martin, and Rafael Paya . Abstract: The aim of this paper is to review the state-of-the-art of recent research concerning the numerical index of Banach spaces, by presenting some of the results found in the last years and proposing a number of related open problems. Archive classification: Functional Analysis Mathematics Subject Classification: 46B20, 47A12 Remarks: 27 pages, 4 figures, to appear in RACSAM The source file(s), KaMaPa.tex: 98692 bytes, adp.eps: 35617 bytes, dp.eps: 34093 bytes, lush.eps: 26434 bytes, norm.eps: 11837 bytes, is(are) stored in gzipped form as 0605781.tar.gz with size 66kb. The corresponding postcript file has gzipped size 167kb. Submitted from: mmartins@ugr.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0605781 or http://arXiv.org/abs/math.FA/0605781 or by email in unzipped form by transmitting an empty message with subject line uget 0605781 or in gzipped form by using subject line get 0605781 to: math@arXiv.org.