Many Council of Trent sessions were held in this bishop's palace/fortress on the north edge of town, which you can reach by walking north from the Duomo along Via Belenzani, and then east on Via Roma (though it's a bit of a trek from the rest of the center and the train station) -- both streets, especially the former, are lined with the palaces, many with faded frescoes on their facades, built to house the church officials who came to Trent to attend the council sessions. The mazelike castello incorporates the 13th-century Castelvecchio, surrounded by medieval fortifications, and the elegant Magno Palazzo, a palace built for a prince-bishop in the 15th century.
Among the many small collections contained within the vast complex is the Museo Provincale d'Arte, where the pride of the collection is the Ciclo dei Mesi (Cycle of the Months), an enchanting fresco cycle painted around 1400. It presents a detailed look at life at court and in the countryside, showing amusements among the lords and ladies and much hard work among the peasants. It's housed in the Torre dell'Aquila, or Eagle's Tower; for admission, ask the guards at the Loggia del Romanino, an atrium named for the Renaissance artist who frescoed it.
You can also visit the cell where native son Cesare Battiste was held in 1916 for his part in the Irredentist movement, which sought to return Trent and other parts of the region to Italy -- which, indeed, came to pass with the Treaty of Versailles in 1919, but not before Battiste was hanged in the moat that surrounds the Castelvecchio.