Harlequin
The Harlequins are the Eldar followers of Cegorach, the Laughing God. They are the performers and entertainers of the Eldar, the self-appointed protectors of the Eldar's pre-fall history, which they perform in extremely elaborate plays. They are also some of the most dangerous shock-troopers among the Eldar, taking the concept of "break a leg" as far as you would expect in Warhammer 40,000. As part of their role as self-appointed keepers of history, they also guard the Black Library from those who would gain entry, allowing only those who have conquered the Chaos within them to enter.
The Harlequins in times of war fight the foes they see as posing a threat to the very existence of the Eldar first and foremost, namely Chaos, the Necrons, and the Tyranids. The Imperials, Tau, and even Orks can be worked with and, unlike most Eldar, the Harlequins are free of racial prejudice, so long as you battle the threats to all things and aren't attacking them/getting in their way, they're perfectly happy to work with you even if you are a Mon'Keigh or Greenskin. Which makes them one of the most levelminded factions in the setting and helps make them a very likeable faction.
The glue that keeps the Eldar together
They owe no allegiance to any Craftworld, Corsair Fleet, Exodite maiden world, or Dark Eldar Kabal, but rather recruit members from all factions, and will fight in the armies on all sides. Their only loyalty is to Cegorach, whom they believe has charged them with the "Great Work" of reunifying the Craftworld Eldar, Corsairs, Dark Eldar, and Exodite Eldar into a single race to fight off Slaanesh, the Necrons, and whoever else has a bone to pick with the chosen of the Old Ones. It is notable that they do not use the methods to keep their souls safe like the others do - their faith in Cegorach, complete after going through the Trial to become a Harlequin, is enough to keep them safe. Despite this, they are allowed free passage through the Craftworlds and Commorragh, because the Craftworld and Exodite Eldar respect the Harlequins for preserving their history, and the Dark Eldar and Corsairs are too afraid to try and stop them find Death Jesters' humor hilarious; they also couldn't keep the Harlequins out if they tried due to the Harlequins superior knowledge of, and ability to use, the Webway.
Eldar Ambassadors?
Notable as xenos to the Imperium as well, since the Harlequins do not restrict their visits to the Eldar - in the Harlequin's view, they must perform their work for anyone and everyone who may benefit and learn the lessons from The Fall, and along the way inspire a little more hope for the galaxy. Thus Harlequin troupes are a frequent sight on Imperial worlds, and exceptionally among xenos, the Imperium allows the Harlequin traveling bands full access to their worlds, as even the High Lords of Terra feel that one can only benefit from the beautiful plays.Citation Needed (The High Lords of Terra also know it'd be impossible to take direct action against Eldar Harlequins as a whole, and maybe bad for their health too.) It's unknown if Harlequins have fought with Imperial units in the past, but there's a reasonable chance they shared the same battlefield against common foes. The Star Leopards Space Marines chapter slapped around a few for desecrating a Land Raider, once, but that was a personal matter. Elaborate in form, but simple in message, the plays allow humans to understand the Great Enemy and what can be done.
Judging from their allies matrix, its fortunate at least humans listen to them, since the Tau worlds they're invited to play on are inevitably met with an endless earful and counters about the fucking Greater Good. They don't play on Necron tombs given that the Necrons are the oldest foes of the Eldar and the two have brought each other nothing but grief over the last few billion years, and Harlequins work to fight against them just as hard as they do against Chaos. Don't even fucking ask if they play on Ork worlds (they probably do, but have to modify the dialogue to grunting and swearing and cockney slang). It's presumed that they did try to play for the Tyranids only once, but found out the space bug-lizards have no appreciation for art; hence why it was decided that they would be added right next to Chaos and the Necrons on the mandate to kill-on-sight-and-annoy-the-hell-out-of.
Solitaires
An interesting note on their plays, only a Solitaire (those delicious women off to the side, though men can become Solitaires too; and according to the new model only men are Solitaires, according to the codex the first Solitaire was a woman, so even if the model is male, females who fill the role too, just like every part of Eldar society. GW is just too lazy to make female versions of HQ models) can play the role of Slaanesh, as attempts by anyone else results in insanity. Generally even loners among the Harlequin, they do not usually travel with a Troupe permanently. Incredibly powerful (even amongst the already crazy powerful Harlequin), the Solitaires are also an anti-psychic madhouse, inspiring psycho like blanks do, and even Eldar psykers feel incredibly depressed in their presence. The truth about their condition is, sadly, even more grimdark. Unlike the others, who are protected by their faith in Cegorach upon their death, the Solitaires are already doomed to be devoured by Slaanesh once they die - this is perhaps what allows them to play Her role in the first place. The only hope they have is Cegorach's last trump card, wherein He is allowed to challenge She Who Thirsts for their souls. He does not always win. However, every time Slaanesh wins, Cegorach was revealed to have lost on purpose, on the count of him replacing the soul in question with a realistic blow-up sex doll while Slaanesh was distracted. As the Prince of Pleasure attempts to fornicate with it, it bursts open, giving him/her/it the coldest of showers that would spoil any excitement he/she/it has built up. It also warps in Khorne for a short while in his realm so he can relive his "Piledriving Slaanesh into oblivion" times during the fall of the Eldar, minus Khaine. Slaanesh, for some reason, keeps falling for it every time.
Want to Join the Harlequins? Then Fuck You
It's not known if recruiting for the Harlequins is done actively, or if they just take in any dispossessed Eldar. And it's not known what sort of criteria they look for (e.g. you're under threat of death by the Autarch for having a genuine sense of humor, the Laughing God is strong with one, etc.). However, any recruit has to pass the trial to become a Harlequin, and it's one of their best kept secrets. A leaked bit of old and probably outdated fluff was that this trial involved becoming possessed by a daemon of Slaanesh and casting it off through sheer willpower. Obviously, the attrition rate was pretty high, with many just getting killed by the process, and even more who succumbed to the possession and were euthanized with a Kevorkian shuriken pistol. However, back in those days, if one was possessed and exorcised, it made one untouchable by Chaos, and thus Slaanesh would lose the claim on that Eldar's soul. Sometimes, however, this process would result in an Eldar losing his soul, but surviving nonetheless. These soulless, pants-shittingly terrifying individuals became the Solitaires. But y'know. Old fluff.
7th Edition
They are currently in the process of being brought into their own army, with new models for all members of the troupe, plus new models and rules for the solitaire and a new Eldar Jetbike, the skyweaver. There are also two new vehicles, the starweaver (a transport) and the voidweaver. In addition, shadowseers are getting their own new psychic discipline, Shadow Phantasmancy. Currently they are battle brothers with the Eldar (both dark and normal, they don't discriminate), allies of convenience with the Imperium and Tau, desperate allies with Orks and come the apocalypse with chaos daemons/marines, necrons and tyranids.
See also: Warhammer 40,000/Tactics/Eldar Harlequins(7E)