in recent years, popa’s deformation/rigidity theory has lead to a wealth of classification and rigidity results for von neumann algebras given by countable groups and their actions on measure spaces. in this talk, i will present the first rigidity and classification results for von neumann algebras given by locally compact groups and their actions. i establish that the crossed product von neumann algebra has a unique cartan subalgebra, when the action is free and probability measure preserving and the group is a connected simple lie group of real rank one, or a group acting properly on a tree. from this, i deduce a w*-strong rigidity result for irreducible actions of products of such groups. i also establish that the group von neumann algebra of such groups are strongly solid. more generally, our results hold for locally compact groups that are non-amenable, weakly amenable and belong to ozawa’s class s. this is joint work with arnaud brothier and stefaan vaes.