A famous problem of Murray and von Neumann (1943) asks whether the II$_1$ factors $L(\Bbb F_n)$ associated with free groups with $n$ generators, $\Bbb F_n$, are non-isomorphic for distinct $n$'s. While this problem is still open, its ``group measure space'' version, showing that the II$_1$ factors $L^\infty(X)\rtimes \Bbb F_n$ arising from free ergodic probability measure preserving actions $\Bbb F_n\curvearrowright X$ are non-isomoprphic for $n= 2, 3, ...$, independently of the actions, has been recently settled by Stefaan Vaes and myself. I will comment on this, as well as on related results by Gaboriau, Ozawa, Ioana, Peterson.