The engineering department or engineering division was a major department aboard Starfleet starships.
The department's name was sometimes shortened to engineering, which might also stand for the main engineering room.
In 2268, Montgomery Scott showed Elaan, the Dohlman of Elas, his engineering department. (TOS: "Elaan of Troyius")
In 2369, William T. Riker denied a request by stellar sciences department head Nella Daren to use the main sensor array a few hours longer, because it had been allocated to engineering, which was running warp field tests. (TNG: "Lessons")
In 2369, Captain Edward Jellico ordered the USS Enterprise-D's warp coil efficiency raised by 15% within two days, which Data opined was possible by utilizing the manpower of the entire engineering department. (TNG: "Chain Of Command, Part I")
Shortly after USS Voyager became trapped in the Delta Quadrant in 2371, there was an altercation in engineering between Maquis and Starfleet crew. Rumor was that the whole department was up in arms, but Tuvok dismissed this as hyperbole. (VOY: "Parallax")