In this talk, I will present several rigidity results for von Neumann algebras of wreath-like product groups. We show that any group G in a natural family of wreath-like products with property (T) is W*-superrigid: the group von Neumann algebra L(G) remembers the isomorphism class of G. This provides the first examples of W*-superrigid groups with property (T). For a wider class wreath-like products with property (T), we show that any isomorphism of their group von Neumann algebras arises from an isomorphism of the groups.  As an application, we prove that any countable group can be realized as the outer automorphism group of L(G), for an icc property (T) group G. This can be viewed as a converse to Connes’ 1980 rigidity theorem asserting that the outer automorphism of L(G) is countable, for any icc property (T) group G. These results were obtained in joint works with Ionut Chifan, Denis Osin and Bin Sun.