I will discuss a new classification result for the unitary representations of oligomorphic permutation groups (or equivalently, automorphism groups of omega-categorical structures, or still equivalently, Roelcke precompact subgroups of S∞). It turns out that every such group has only countably many irreducible representations and it is possible to describe them quite explicitly. This recovers older results of Lieberman about S∞ and Olshanski about the linear group of an infinite-dimensional vector space over a finite field. We also establish property (T) for many of those groups.