Bernoulli shifts over amenable groups are classified by entropy (this is due to Kolmogorov and Ornstein for $Z$ and Ornstein-Weiss in general). A fundamental property is that entropy never increases under a factor map. This property is violated for nonamenable groups. In spite of this, sofic entropy theory makes sense even for nonamenable groups and Bernoulli shifts are classified by sofic entropy. Time permitting, I'll also discuss recent results of B. Seward showing how Rohlin entropy can be used to extend this classification to all countable groups (conditional on a natural conjecture).