There are 2 basic kinds of Wolftrap Anglers, each with their own genus. They are Lasiognathus and Thaumatichthys. One thing they share, and which gives them their name, is their extraordinary mouths. The lower jaw is quite short, with short teeth. This is all relative of course. Anglerfish are famed for their massive maws and these lower jaws are by no means short, it's just that the upper jaw is utterly shocking. It's significantly longer and wider, with these kind of "lips" that can close down around the lower jaw. They aren't lips, they're called premaxillaries. There's bone in there, and the edges are lined with long, curved or even hooked teeth. It's akin to our very own Venus Flytrap... Venus Wolftrap, perhaps. It's like their upper jaw has it's own downward facing jaws. Ick.
Lasiognathus have an esca at the end of a long illicium (lure at the end of a fishing rod). The esca is bioluminescent and even has hooks on it, leading to all sorts of theories as to how it's used, including ideas of it being cast forward and used to impale prey. Nice idea, but it might not be necessary - a bait with some nearby jaws may well be enough to capture the small, bony fish that make up their diet. Speaking of which, there are 5 known species of Lasiognathus, the longest of which is 15.7 centimetres, the smallest is half that. They have been found in various locations scattered across the Atlantic and Pacific Oceans at depths of about 4,000 metres (13,100 feet). All this is the female, no male has yet been discovered.
View from the bottom and top.
Thaumatichthys are a little different. Here, the illicium is upside own and backwards so that the esca hangs down from the roof of the mouth like a chandelier. There are also little bumps in there which act as taste buds. Oh dear. Little animals hoping for a cosy, fireside resting place will realise their mistake when those upper jaw jaws close around them. Thaumatichthys are unique among deep sea anglers in that they are bottom feeders, which I guess is why they are so flattened in shape. They also seem to be omnivorous, even eating plant matter. There are three species so far, the biggest found was 36.5 cm long and found 3,600 m (11,800 feet) down. Another was just under a foot long and the third is known from just one 6 cm specimen. These are found at depths between 1,000 and 2,000 m (3,300-6,600 ft) and they are all from tropical waters worldwide. The biggest male discovered is 45 millimetres long and is armed with not much more than great, big olfactory organs for a great, big sense of smell. It's not known whether he's parasitic to the female, but it doesn't look unlikely.