The Prince-Archbishopric of Bremen — not to be confused with the modern Archdiocese of Hamburg, founded in 1994 — was an ecclesiastical principality (787–1566/1648) of the Holy Roman Empire and the Catholic Church that after its definitive secularization in 1648 became the hereditary Duchy of Bremen. The prince-archbishopric, which was under the secular rule of the archbishop, consisted of about a third of the diocesan territory. The city of Bremen was de facto and de jure not part of the prince-archbishopric. Most of the prince-archbishopric lay rather in the area to the north of the city of Bremen, between the Weser and Elbe rivers. Even more confusingly, parts of the prince-archbishopric belonged in religious respect to the neighbouring Diocese of Verden, making up 10% of its diocesan territory.

In the Holy Roman Empire, the German term Hochstift referred to the territory ruled by a bishop as a prince, as opposed to his diocese, generally much larger and over which he exercised only spiritual authority. The terms prince-bishopric and ecclesiastical principality are synonymous with Hochstift. Erzstift and Kurerzstift referred respectively to the territory (prince-archbishopric) ruled by a prince-archbishop and an elector-archbishop while Stift referred to the territory ruled by an imperial abbot or abbess, or a princely abbot or abbess. Stift was also often used to refer to any type of ecclesiastical principality.