Notably, Mützenich is a German exclave surrounded by Belgian territory due to the track bed of the former Vennbahn railway line being part of Belgium following the implementation of the Treaty of Versailles, among other small areas.

Mützenich is located on the German-Belgian border, in the region of the High Fens and below Steling mountain, at 584 m above NHN.

In 1952, of 53 people indicted for smuggling, 47 were convicted (four were acquitted and the proceedings against two women were dismissed due to insignificance).

Aviation pioneer Erich Offermann [de] (1885–1930) raised a hill near Mützenich for flight experiments which started in 1910.

[5] There are several guesthouses, hotels and restaurants in Mützenich, retail stores and other trades, as well as milk and meat farmers.

Some of Monschau's listed historic monuments are located in Mützenich, such as the Catholic church of St. Bartholomew (St. Bartholomäus in German).

A landmark about one kilometre north of the village is Kaiser Karls Bettstatt ("Emperor Charlemagne's resting place"), a slab of quartzite near Steling mountain and by one of the major tracks into the High Fens.