A famous result of Ornstein and Weiss fully classifies Bernoulli systems over Z in terms of the entropy of the base space. It was a few years later extended to the situation where Z is replaced by any amenable group, but for example for the free group the analogous problem was open until 2010, when it was finally solved by Lewis Bowen. I will discuss the complications arising in the non-amenable setting, present the crucial notion of mean sofic entropy introduced by Bowen and discuss some further, very recent, related developments.