In 1958, Kolmogorov defined the entropy of a probability measure preserving transformation. Entropy has since been central to the classification theory of measurable dynamics. In the 70s and 80s researchers extended entropy theory to measure preserving actions of amenable groups (Kieffer, Ornstein-Weiss). I'll explain a generalization of Kolmogorov-Sinai entropy to actions of free groups and more generally, sofic groups. Applications include the classification of Bernoulli shifts over a free group, answering a question of Ornstein and Weiss.