  Kolmogorov-Sinai entropy is an invariant of measure-preserving actions of the
group of integers that is central to classification theory. There are two
recently developed invariants, sofic entropy and Rokhlin entropy, that
generalize classical entropy to actions of countable groups. These new theories
have counterintuitive properties such as factor maps that increase entropy.
This survey article focusses on examples, many of which have not appeared
before, that highlight the differences and similarities with classical theory.
