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 this expository paper. In addition to a statement and proof of Ioana's theorem, this paper features the following: (i) an introduction to rigidity, including a crash course in Borel cocycles and a summary
of some of the best-known superrigidity theorems; (ii) some easy applications of superrigidity, both to ergodic theory (orbitβ¦Β CONTINUE READING