The Unicomplex was a vast Borg complex composed of thousands of connected structures and hubs spanning at least 600 kilometers, that housed hundreds of Borg ships and trillions of drones. (VOY: "Dark Frontier")
It was considered, by the independent drones, to be the home of the Borg Queen. (VOY: "Unimatrix Zero") This complex is likely the closest thing that the Borg have ever had to a physical capital or headquarters.
The Unicomplex came under attack in 2375, when Kathryn Janeway, Tom Paris, Tuvok, and The Doctor took the Delta Flyer to rescue Seven of Nine, who was blackmailed into leaving the crew of the USS Voyager. (VOY: "Dark Frontier")
The Unicomplex was severely damaged and possibly destroyed in 2378, after the Borg Queen assimilated a neurolytic pathogen from the future Admiral Janeway, who had traveled back in time to bring Voyager home. (VOY: "Endgame")
Background information Edit
It is unclear whether there was more than one Unicomplex. In VOY: "Unimatrix Zero, Part II", the Borg Drone Axum suggested that the independent drones attack the "Primary Unicomplex," implying that there are other, smaller unicomplexes.
When the Unicomplex was introduced in the script of "Dark Frontier", it was described thus: "A vast infrastructure of interconnecting modules, grids, technology -- a 'metropolis' floating in space as far as the eye can see. Dozens of Borg Cubes and Spheres and other Geometric Shapes are flying around the perimeter. This is the sum total of Borg Perfection -- a purely technological world."
The construction of the Unicomplex had an unusual starting point. Visual Effects Supervisor Mitch Suskin explained, "We started the Unicomplex with some building blocks that [Visual Effects Producer] Dan Curry laid out, which were literally built out of two blocks of wood and some Tinker Toys in his garage." (Cinefantastique, Vol. 31, No. 11, p. 33) Curry was intent on ensuring that the Unicomplex had an atypical shape that was nevertheless consistent with Borg design. (Star Trek: The Magazine Volume 1, Issue 1, p. 56)
The job of modeling the Unicomplex with CGI, digitally reconstructing Dan Curry's maquette, was mostly achieved by Foundation Imaging staffer Koji Kuramura. (Star Trek Monthly issue 58, p. 44) However, this task proved to be a difficult one. Remembered Mitch Suskin, "The real thing, putting it in Borg space, making it look big enough, making it have enough detail, and rendering it, was nightmarish." (Cinefantastique, Vol. 31, No. 11, p. 33) Foundation Imaging's Adam "Mojo" Lebowitz commented, "It was probably the biggest model, polygon-wise, memory-wise, that we've ever had to do for Star Trek. So it was a real trick to photograph it. They were really pushing our machines to the limit of what they could do. We had to break things up into multiple tasks. We would actually delete any part of the Unicomplex that wasn't seen by the camera from the screen to save memory [....] One of the animators added a little rail system that went through in one shot just to bring it to life. And we did some nice dark lighting on it to make it look pretty." (Star Trek Monthly issue 58, p. 44)
Although lack of perspective in most exterior shots of spacecraft normally meant that moving the camera seemed as thought the craft itself was instead moving, the multi-layered structure of the labyrinthine Unicomplex allowed for more freedom of the kinds of viewpoints that could be selected. "With this huge Borg Unicomplex with all this perspective at contiguous levels," remarked Lebowitz, "you could move the camera into a crane shot. We were able to do those kinds of shots in 'Dark Frontier' because of that model, and normally we can't. That was actually one of the first things I got excited about when we saw Dan [Curry]'s design. I knew we would be able to do some nice camera moves that we often can't do in space." (Star Trek Monthly issue 58, pp. 44-45)