Let G be a locally compact group and LG the group von Neumann algebra of G. In this talk I will discuss certain properties of G which are visible/invisible on the level of LG. In particular property (T), Haagerup property and amenability will be discussed. I will also explain the Tatsuuma duality for G. In the second part of the talk (which is based and the joint work with M. Daws, A. Skalski and P. Sołtan), the Herz restriction theorem in terms of group von Neumann algebras will be formulated and its relatively simple proof will be given.