They've been kept a few times (I think 3 so far?) in Japanese aquariums, but always only surviving for a very short period. I think the last one was at Numazu Deep Sea Aquarium last year. In addition to the general issues with keeping deep sea fish, one of the problems is that the few frilled sharks that have ended up in aquariums have invariably been damaged. Either sick animals found in shallow waters or incidentally caught by fishermen and pulled up relatively fast from the depths. Basically the same as the few goblin sharks that have been displayed for short periods.
Only a handful of deep sea animals have been kept in captivity.
A
very big handful by now, though truly bathyl and abyssal species (restricted to depths below 3300 ft; 1000 m) remain largely out of reach. The pressurized "
Abyss Box" at Brest is still alone in the public aquarium world.
I always thought it would be cool to have a whale fall exhibit, where there's a fake whale carcass and some live animals you might see in a whale fall.
Quite remarkable indeed and already done at Enoshima in Japan where in an aquarium (
photo page 61) that also features a hydrothermal vent and cold seep. I've always hoped that an aquarium eventually would display a colony of the giant worm
Riftia pachyptila, but so far we'll have to do with the related
Lamellibrachia in Japan.
If deep sea creatures could be kept more easily, I could get sleeper sharks and giant isopods.
Giant isopods are fairly easy to keep and kept several places around the world. Most are in Japan, but some elsewhere too (Singapore, Berlin, etc).
Sleeper sharks range from very deep water to shallow water, so pressure isn't an issue at all. To my knowledge, no one has tried, but in all probability it would be easy enough if you had a large aquarium kept at very cold temperatures. It is expensive to chill water. I'm not aware of any aquarium in the world with a cold water tank (up to 40°F; 5°C) that is anywhere near the size necessary to even consider a sleeper shark. Sevengill sharks, which in many ways are quite similar, are easy enough to keep, but they do have the advantage that they're fine with warmer temperatures.
Various lanternfish and plankton, and firefly squid.
Flashlightfish are kept several places around the world, but they require complete darkness to really flash. However, there are a several places that do keep them in ways where the flashing can be seen well (check this
video from Numazu Deep Sea Aquarium). It's the same with pinecone fish and while many aquariums keep those, few keep them in ways where the flashing can be seen well. Just like flashlightfish, some species of lanternfish move from deep water towards shallower water in dark nights, so they could probably be kept in a similar way, except in somewhat colder water.
The various types of glowing plankton generally only do it in responce to touch or sudden water movement (it's suspected to be a defensive strategy) and it would be hard to replicate this in captivity. I suspect they'd eventually turn off the light for good if they were bugged all the time. Some of these aren't retricted to deep water either: For example, many people, myself included, have had a pleasure of seeing the remarkable glow of
Noctiluca scintillans in late summer evenings.
In addition to the fish, there are already several aquariums around the world with fluorescent corals, glowing crystal jellyfish and comb jellies, electric flame scallops (which however have an awful survival record in captivity),
Euprymna bobtail squid, etc. Even if limiting it to species that are kept today you can get a very interesting series of exhibits.
At least part of it is likely temperature. Basking sharks prefer 45–60°F (8–15°C). There are several aquariums around the world with quite large tanks that are kept temperate or subtropical, but the truly massive tanks (at least 2 mio gallon/7.5 mio l) are all tropical; 70–78°F (22–25°C). Here I only include tanks aimed at fish, not tanks made for sea mammals like walruses or orcas. In case people wonder, the current massive fish tanks, roughly in order of size are at Georgia (USA), Chimelong Ocean Kingdom (China), S.E.A Aquarium (Singapore), The Lost Chambers (United Arab Emirates), Dubai Aquarium (United Arab Emirates) and Okinawa Churaumi (Japan). These are all tropical. They are followed by more than a dozen aquariums in USA, Europe, Asia and South Africa with large tanks in the 1–1.9 mio gallon (3.8–7 mio l) range, including tropical, subtropical and temperate.
You could probably keep a basking shark in a tank below 2 mio gallon (7.5 mio l), but the ethics would be questionable. There are records of basking sharks in tropical regions, but they are generally far between, generally seasonal, or generally in regions where it is suspected that they spend much of the time deep (where the waters are fairly cold, even in the tropics).
So, let's assume an aquarium made a massive fish tank and kept it at temperate/subtropical temperatures. This would exclude many of the species typically displayed in ocean tanks because they are unable to survive long-term in colder waters. However, you could actually get a quite remarkable collection of species. If kept at the upper temperature range (circa 60°F; 15°C) preferred by basking sharks, other suitable species would be spotted and gulf wobbegongs, angelshark, broadnose sevengill shark, common thresher shark, sandtiger shark, copper shark, smooth hammerhead shark, short-tail and thorntail stingrays, various
Myliobatis eagle rays, European conger, bluefin tuna, swordfish, ocean sunfish, and a host of smaller species. I would definitely be interested in visiting that aquarium! As far as I know, neither thresher shark nor swordfish has been kept in captivity and their specialized hunting techniques may cause problems, but they would certainly be remarkable.