Abstract: The Haagerup property, or a-T-menability, is a particularly interesting weak form of amenability. Unlike amenability, it is not stable under semi-direct products and it is an open question, given an action of a group $G$ by automorphisms on a group $N$ to give conditions ensuring the Haagerup property for the semi-direct product $N\rtimes G$. In this talk, we will consider special semi-direct products, namely permutational wreath products $H\wr_X G$ (where $X$ is a $G$-space) and we will sketch the proof of the following result. Assume that $X$ is a quotient {\it group} of $G$. Then $H\wr_X G$ has the Haagerup property if and only if $H, G$ and $X$ do have it (one direction is due to Chifan and Ioana, the other to Cornulier, Stalder and myself).