There are plenty of shallow-water anglers such as frogfish, which are wonderful residents of an appropriate tank, but the true "deep-sea" fishes haven't ever (to my knowledge) been kept for more than a few moments in a glass box.
At the public aquarium I work at on weekends, we used to have a deepwater tank which featured New England red crabs, hagfish, and giant isopods. Sort of like a 'pod from your tank, but about the size of a junior football. Very cool display, decorated with a few bones from a dolphin skeleton that'd washed up, and a cast of a pygmy sperm whale's skull.
~Bruce