In the theory of C*-algebras, the extensions play a fundamental role because they generate the cycles of bivariant K-theories (in particular those of K-homology). A group G is said to have property T of Kazhdan if every continuous affine action of G on a real Hilbert space has a fixed point. This “rigid” behavior is opposite in a sense to that of similar actions of amenable groups. The main goal of the talk is to discuss, following the 1991 Annals paper of Simon Wassermann, how property T can be used to provide examples of non-invertible extensions. The needed facts related to extensions and property T will be also covered.