This is an announcement for the paper "$H^{\infty}$ functional calculus and square functions on noncommutative $L^p$-spaces" by Marius Junge, Christian Le Merdy and Quanhua Xu. Abstract: In this work we investigate semigroups of operators acting on noncommutative $L^p$-spaces. We introduce noncommutative square functions and their connection to sectoriality, variants of Rademacher sectoriality, and $H^\infty$ functional calculus. We discuss several examples of noncommutative diffusion semigroups. This includes Schur multipliers, $q$-Ornstein-Uhlenbeck semigroups, and the noncommutative Poisson semigroup on free groups. Archive classification: Functional Analysis Mathematics Subject Classification: Primary 47A60; Secondary 46L55, 46L69 Remarks: 118 pages The source file(s), JLX.tex: 355560 bytes (looks big), is(are) stored in gzipped form as 0601645.gz with size 94kb. The corresponding postcript file has gzipped size 394kb. Submitted from: qx@math.univ-fcomte.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0601645 or http://arXiv.org/abs/math.FA/0601645 or by email in unzipped form by transmitting an empty message with subject line uget 0601645 or in gzipped form by using subject line get 0601645 to: math@arXiv.org.