This is an announcement for the paper "Compact and weakly compact composition operators from the Bloch space into M\"obius invariant spaces" by Manuel D. Contreras, Santiago Diaz-Madrigal, and Dragan Vukotic. Abstract: We obtain exhaustive results and treat in a unified way the question of boundedness, compactness, and weak compactness of composition operators from the Bloch space into any space from a large family of conformally invariant spaces that includes the classical spaces like $BMOA$, $Q_\alpha$, and analytic Besov spaces $B^p$. In particular, by combining techniques from both complex and functional analysis, we prove that in this setting weak compactness is equivalent to compactness. For the operators into the corresponding ``small'' spaces we also characterize the boundedness and show that it is equivalent to compactness. Archive classification: math.FA Mathematics Subject Classification: 47B33 Submitted from: dragan.vukotic@uam.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1307.5784 or http://arXiv.org/abs/1307.5784