Other forms: duchies
If you are a duke or a duchess, the country or territory you rule is called a duchy. England's Prince Charles is the current Duke of Cornwall and symbolically reigns over a duchy that includes Cornwall and the surrounding area.
The term duchy is mainly historical and almost always refers to European territories. Over the years, many dukes and duchesses have ruled over duchies, while others have maintained honorary titles without any real power. Grand duchies were small, sovereign countries ruled by a grand duke or grand duchess. Today, the only remaining grand duchy is Luxembourg, symbolically ruled by Grand Duke Henri, who has limited governmental powers.