Zoanthrope
The Zoanthrope is a Tyranid species characterised by its massive head, a long thin body dangling under it and having enough psychic power to turn a Land Raider inside out.
Physiology
Prior to third edition, Zoanthropes looked like giant two-legged Zoats. Yes, this was utterly stupid and was retcon'd with extreme prejudice.
The Zoanthrope is a tall, slender creature with an oversized cranium that makes up more than half its mass and about half its body length. The Zoanthrope's head is far too large for its body: if it were a natural creature its neck would snap under the weight of the noggin. But the Tyranids do not obey the laws of nature: the massive brain housed by the head serves as a relay for the massive psychic power of the Hive Mind, giving the Zoanthrope awesome psychic powers. What powers you ask? How about the power of flight? That do anything for ya? That's levitation, Holmes. How about the power to kill a yak, from 200 yards away... with mind bullets! That's telekinesis, Kyle. How about the power... to move you?
(ahem)
Sorry for that. But Tenacious D did all but perfectly describe the Zoanthrope's abilities in their song Wonderboy. With their powers they can float (but not that high off of the ground), they can shoot holes the size of a Predator Tank in a Predator Tank (or melt small groups of MEQs), and have the power to move you. With "you" meaning "your creatures that have Instinctive Behavior" because the Zoanthrope is a Synapse Creature. It also has a strong forcefield surrounding it, meaning that it has a good chance to shrug off otherwise lethal shots. And in older editions there were almost as good as Warriors at fighting. Like any Psyker, the Zoanthrope is vulnerable to brain overload and subsequent exploding craniums (or as Orks call it; 'eadbanging). If this happens the creature's brains burn out and it falls to the ground like a grotesque deflating balloon.
One Zoanthrope called "The Doom of Malan'tai" evolved to feed on psychic energy. It got the name after singlehandedly destroying Craftworld Malan'tai when it drained the Infinity Circuit. But according to recent developments this creature has been thought to be the progenitor of a new sub-species of Zoanthrope called the Neurothrope.
On the tabletop
Zoanthropes are used best against either vehicles, tough armoured models, or big monsters where they can simply ignore toughness and armour saves with impunity. In 8th edition they have access to three powers: the tank-wrecking Warp Blas-er, 'Smite', and one power that you can choose / roll for from the Tyranid powers table. The downside to this is that they can only attempt to manifest one power each turn, unless the unit numbers four or more models. However, their Smite does get a step up from that of other lesser psykers since - if the unit contains four or more models - it does 2D3 mortal wounds rather than D3. Once again, the larger the unit the better - it's almost like Games Workshop wants to push us to buy more models...
Because of the short range of their powers they have to come dangerously close to their target. This is why you should always provide enough distractions so they are not shot to death in one turn. As they are Synapse Creatures, they will keep your Gaunts controllable, which is always nice but again remember the range on their weapons and that they are not as fast as Hormagaunts. And while a single shot is likely to deal great damage to a single target, it is not guaranteed it will be destroyed: as such it is smart to take several of these in a single brood.
They also have a good invulnerable save and a lot of wounds, which makes them a good bodyguard for characters. The Neurothrope itself makes a better-than-average warlord, too, for the same reason. Just don't expect it to kill anyone in melee.
Tyranid players rejoice! With the new update, they can deep-strike again using the Tyrannocyte, which makes them even more awesome. Buy a nice bug-balloon, stuff it with Zopes, and drop it behind whatever scares you for instant gratification.
Some things of note come up with these unique psychic smile-inverters. First, now that we're in 8th edition, despite having a 3+ invulnerable they do still benefit from their brother-from-another-mother Venomthropes thanks to the rewritten Shrouding Spores rule, so it may be worth buddying the floating snake 'nids up if you want your Zoanthropes to have that extra bit of protection. Second, their 'Warp Blast' (okay, so it's really Smite, but I've been calling it Warp Blast for five editions damnit and I'm not going to stop now!) power is a Warp Charge 5 attack. This means that they have a majority chance of success, but it's also much easier to deny nowadays due to the 8th edition Deny The Witch. Keep them away from enemy psykers and they should be good to go. Third, at least as of release, the Neurothrope upgrade is free now. Given that this beastie lets the unit regain wounds after Smiting someone, it's a no-brainer.
In Last Stand
In Last Stand, these things are assholes: Giant, flaming assholes. They do enormous damage, have immense knockback, a huge area-of-effect, and are remarkably durable for a floating snake-brain thing thanks to a Warp Field that acts like an Iron Halo. They are the bane of every Lord General, since they can effectively one-shot the entire minion squad a General may have with him. They are, thankfully, easy prey for Sniper Rifle rounds and Shotgun solid slugs, and are a perfect target for a Chaos Sorcerer who has the Improved Summoning wargear to clone.