The Council of Trent, the 19th of the 21 ecumenical councils recognized by Roman Catholicism, is called the Tridentine council, and the dogmas defined by the that council are called Tridentine dogmas.
The word Tridentine is also used to describe conservative Roman Catholic members who reject many of the reforms of the two later councils, especially the Second Vatican Council, most notably the Novus Ordo (New Mass of Pope Paul VI) and who instead remain attached to the theology, liturgy and ceremonial of pre-Vatican II Roman Catholicism. While some Tridentine Catholics remain part of Roman Catholicism (often celebrating the Novus Ordo in Latin) many are attached to breakaway movements such as the Society of St. Pius X or the true Catholic Church. Such groups place particular stress on the celebration of the Tridentine Mass, instituted at the Council of Trent, whose celebration is now prohibited by the Vatican except with special permission.1
Some Tridentine Catholics who belong to sedevacantist movements have gone so far as to elect their own 'popes'. The Montana-based true Catholic Church in 1998 elected Reverend Father Earl Lucian Pulvermacher, OFM Cap to the papacy, which it argued had been vacant since the death of Pope Pius XII in 1958. Pulvermacher was proclaimed Pope Pius XIII.
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1 After being heavily restricted, the celebration of the Tridentine Mass is now being allowed more frequently. In 1999 a full Pontifical High Mass was celebrated by a visiting cardinal in St. Patrick's Cathedral, New York in front of an invited congregation that included the late Cardinal O'Connor. In 2002 it was revealed that the Tridentine Mass is now being celebrated (though not on the main altar) in St. Peter's Basilica in the Vatican. Pope John Paul II has also celebrated Masses according to the Tridentine Rite in his private chapel in the Apostolic Palace.