The Haagerup property (HAP) for a locally compact group G can be characterised via the existence of a specific (mixing and weakly containing the trivial representation) representation of G. On the other hand property (T) is introduced via a property of all representations of G. In this talk I will recall these (and some other) characterisations and present another relatively recent approach which describes both HAP and (T) in terms of `typical' representations of G or `typical' actions of G on a probability space (partly based on the work of Hjorth, Kerr and Pichot, partly on a recent joint article with M. Daws, P. Fima and S. White).