This is an announcement for the paper "Compactness in Banach space theory - selected problems" by Antonio Aviles and Ondrej F.K. Kalenda. Abstract: We list a number of problems in several topics related to compactness in nonseparable Banach spaces. Namely, about the Hilbertian ball in its weak topology, spaces of continuous functions on Eberlein compacta, WCG Banach spaces, Valdivia compacta and Radon-Nikod\'{y}m compacta. Archive classification: math.FA math.GN Submitted from: kalenda@karlin.mff.cuni.cz The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1005.4303 or http://arXiv.org/abs/1005.4303