\indent From every countable group G or measure preserving action of G on a probability space X, one can construct a von Neumann algebra. A central theme in the theory of von Neumann algebras is understading how much of the group or group action is ``remembered'' by its von Neumann algebra. In this talk, I will survey recent results which provide the first classes of groups and group actions that can be completely recovered from their von Neumann algebras.