I will present recent joint work with Arnaud Brothier on actions of locally compact groups on von Neumann algebras. We study algebraic properties of the associated crossed-product algebras, and prove among other things a correspondance result between certain subalgebras of this crossed-product and closed subgroups of the acting group. This generalizes results of Izumi-Longo-Popa. I will explain our (very different) approach, and give related questions and conjectures.