  In this expository article, we give a survey of Adrian Ioana's cocycle
superrigidity theorem for profinite actions of Property (T) groups, and its
applications to ergodic theory and set theory. In addition to a statement and
proof of Ioana's theorem, this article features:
  * An introduction to rigidity, including a crash course in Borel cocycles and
a summary of some of the best-known superrigidity theorems;
  * Some easy applications of superrigidity, both to ergodic theory (orbit
equivalence) and set theory (Borel reducibility); and
  * A streamlined proof of Simon Thomas's theorem that the classification of
torsion-free abelian groups of finite rank is intractable.
