The first Catholic Inquisition started in 1184 in southern France and ended as Catharism disappeared. There was also the Roman Inquisition which started in 1542 and the Spanish Inquisition, which started in 1478. You can read more about it at http://www.catholic.com/tracts/the-inquisition.
It continues today, in the form of the Supreme Sacred Congregation of the Holy Office, a part of the Roman Curia. They do not torture. They make inquiry of the doctrinal and moral fitness of instruction provided by their own people, and remind the faithful of the truth of the faith. The Pope appoints a cardinal to preside over the Congregation, which usually includes ten other cardinals, as well as a prelate and two assistants, all chosen from the Dominican Order. The "Holy Office" also has an international group of consultants, experienced scholars in theology and canon law, who advise it on specific questions.