Murat is situated on the eastern edge of the Mounts of Cantal, in the valley of the Alagnon, a tributary of the Allier, which was the principal route for crossing the Massif Central. It is surrounded by three basalt outcrops, the vestiges of former volcanoes, the Rocher de Bredons, where there is a priory church dating from the 12th century, the rocher de Bonnevie, where there is an 8-metre high statue of the Virgin Mary known as Notre-Dame de la Haute-Auvergne, and the Rocher de Chastel, where the 12th century chapel of St Antoine stands. A market is held every Friday.