c. 1200, "debauchery, extravagance, wanton living," from Old French riote (12c.) "dispute, quarrel, (tedious) talk, chattering, argument, domestic strife," also a euphemism for "sexual intercourse," of uncertain origin. Compare Medieval Latin riota "quarrel, dispute, uproar, riot." Perhaps from Latin rugire "to roar." Meaning "public disturbance" is attested by late 14c. Meaning "something spectacularly successful" first recorded 1909 in theater slang.
To run riot is first recorded 1520s, a metaphoric extension from Middle English meaning in reference to hounds following the wrong scent. The Riot Act, part of which must be read to a mob before active measures can be taken, was passed 1714 (1 Geo. I, st.2, c.5). Riot girl and alternative form riot grrl first recorded 1992.