An embassy is a building where diplomats from one world can live and/or work on the territory of another. Many worlds have embassies on Earth, which is the capital of the United Federation of Planets. A consulate is a sub-division of an embassy.
During the 22nd century, the Vulcans had consulates in Berlin, Canberra and San Francisco. (ENT: "Fusion", "Terra Prime")
The Earth embassy on Vulcan was bombed in 2154. (ENT: "The Forge")
Early in his Obsidian Order career, Elim Garak was posted to the Cardassian embassy on Romulus. According to Garak, however, he was merely a gardener there. (DS9: "Broken Link")
- According to a line cut from DS9: "The Wire", Benjamin Sisko was also assigned to Romulus, when he was posted at the Federation embassy there during the late 2350s.
Lisa Cusak once worked at the Federation embassy on Andor. While there she started a long relationship with an Andorian who worked at the Andorian Agricultural Ministry. (DS9: "The Sound of Her Voice")
One of Odo's friends in Starfleet Intelligence was formerly assigned to the Federation embassy on Qo'noS. This friend of Odo's still had a contact with a former agent of Klingon Intelligence. (DS9: "Visionary")
Gul Dukat suggested that if he was to get his position back as Military Advisor to the Detepa Council, he would post Gul Marratt to the Cardassian embassy on Breen in 2372. (DS9: "Return to Grace")
In 2374, the Orion Syndicate planned, attempted and failed an attempt to break into the Klingon embassy on Farius Prime to assassinate their Ambassador. (DS9: "Honor Among Thieves")