  This is a survey of methods of proving or disproving the Rapid Decay property
in groups. We present a centroid property of group actions on metric spaces.
That property is a generalized (and corrected) version of the property
(**)-relative hyperbolicity" from our paper with Cornelia Drutu, math/0405500,
and implies the Rapid Decay (RD) property. We show that several properties
which are known to imply RD also imply the centroid property. Thus uniform
lattices in many semi-simple Lie groups, Artin groups of large type and the
mapping class groups have the centroid property. We also present a simple
"non-amenability-like" property that follows from RD, and give an easy example
of a group without RD and without any amenable subgroup with superpolynomial
growth, some misprints in other sections are corrected.
