|• Mayor||Kristina Franke|
|• Total||39.70 km2 (15.33 sq mi)|
|Elevation||19 m (62 ft)|
|• Density||150/km2 (400/sq mi)|
|Time zone||CET/CEST (UTC+1/+2)|
It is situated on the south side of the Flensborg Fjord, an inlet of the Baltic Sea, approx. 10 km northeast of Flensburg. The town was originally the home of the family Schleswig-Holstein-Sonderburg-Glücksburg (or simply Glücksburg), since 1863 the royal family of Denmark and since 1905 of Norway. A branch of the family is the former royal family of Greece, which includes Prince Philip, Duke of Edinburgh. His descendants, including Charles, Prince of Wales, Prince William, Duke of Cambridge, and Prince George of Cambridge, are members of the House of Windsor under British law, but genealogically are members of a cadet branch of the House of Glücksburg.
Glücksburg is home to a German Navy base. Among the facilities at the base is the transmitter, callsign DHJ58. DHJ58, situated at 54° 50'N and 9° 32' E, ceased its transmissions on longwave frequency 68.9 kHz in 2002 and in 2004 its longwave antenna was disassembled. Since 2016, the place-name signs have been German and Danish: under the German name "Glücksburg", the Danish name "Lyksborg" is emblazoned.