Be'lakor the Dark Master is the first (and debatably only) Daemon Prince of Chaos Undivided. Of course, this claim of "Only" is suspect with the unclear status of Lorgar and Perturabo's alignments, as well as whether Nemeroth's still alive. Bellator means warrior in
Latin High Gothic.
Due to his nature as a daemon prince of chaos, he's been sighted in both Warhammer Fantasy Battles as well as Warhammer 40,000. In both, he began as an ancient warlord from ages past who fought in the name of the Chaos Gods before they decided to elevate him as a Daemon Prince. Then he got cocky, thought himself better than his four owners, and then got royally bitchslapped back into line.
Be'lakor was one of the earliest Chaos warlords, leading vast hordes of Daemons to ravage the world long before the Elves rose up against them. He impressed the Chaos Gods so much they turned him into a Daemon Prince, the first time they ever did that to a mortal follower of Chaos Gods. However, his four parents began bickering for ownership, each offering some presents in exchange for his loyalty. He decided to then take all their presents and fled to the mortal realms without doing any of their favors. He came during the First Great War Against Chaos, bending many to his will and carving a warpath - unwittingly carrying out the tasks the four set before him. As time carried on, more Daemon Princes were raised, siphoning the power and attention that was once exclusively his and eventually sparking a great war as these new princes sought to carve out territory. This distracted team Chaos from stopping the elves in Ulthuan from creating the Great Vortex, thus stemming the tide of badstuffs spilling into the world.
As punishment, the big four made him become the one to crown Everchosens of Chaos while never getting to become the Everchosen himself, which pissed him off to no end. This is a retcon though, as originally Be'lakor got arrogant and thought he was better than the Chaos Gods, so Tzeentch served him a big piece of humble pie by denying him a physical body and forcing him to crown each Everchosen. At one point Be'lakor co-opted this by possessing one of the Everchosen candidates (who became known as the Shadowlord), but Be'lakor's power destroyed the host body and he was stuck back in the role. In the expansion Shadows of Albion, Be'lakor was the main bad guy there, manipulating people to take the power and artifacts of Albion for himself, before failing and abandoning that plan.
With the latest Everchosen, Archaon, Be'lakor was once again forced to crown the Everchosen of Chaos with the final artifact. Be'lakor played a big part in the Storm of Chaos campaign, but that has since been retconned. Although he still shows up from time to time, he no longer appears to be quite as powerful as he once was, although he is still a Daemon Prince of Chaos Undivided, which is a massive accomplishment in and of itself. In newer lore, he also took the form of a Norse warlord who conducted a raid on a Nordlander town where he raped a woman and fathered a child who would go on to become Archaon.
During The End Times, Be'lakor was all set to return to his former glory and then some, plotting to become the fifth Chaos God by breaking into Kazad Drengazi, the Fortress of the First Slayer (Grimnir, natch), a temple containing the Chaos Gate that Grimnir used to get to the Realm of Chaos in the first place. Be'lakor used the power of the Chaos Gate to break Tzeentch's curse, regain his physical form, and summon four greater daemons, one of each of the Chaos Gods; two of them had had their shit ruined by Gotrek and Felix once before. Be'lakor and his posse planned to backstab Grimnir from behind, at which point Be'lakor would take all of Grimnir's power and ascend to become the fifth Chaos God, but Gotrek and Felix showed up and wrecked Be'lakor and the Bloodthirster, while Grimnir kicked the asses of the Keeper of Secrets, Lord of Change, and Great Unclean One. It looked like Be'lakor and Gotrek's duel could go either way at first, then Gotrek hit Be'lakor with the Bloodthirster and kicked all their asses back to the Realm of Chaos, ruining Be'lakor's plans.
He later caused mischief in Athel Loren by manipulating the Khainites and the more xenophobic forest spirits to attack the elves, but got driven away by the elves armies and the new Incarnate of Light - Tyrion. Though he did play a major role in dooming the world by freeing Mannfred von Carstein from his imprisonment and ensuring the Chaos Gods learnt of Lileath's haven. During his attempt to slay Lileath and consume her divine power, he got captured by Malekith, interrogated under threat of being Nagash's guinea pig if he didn't co-operate and was then trapped in a magic ruby by Alarielle for the rest of eternity. One true Everchosen my ass!
Age of Sigmar
Somehow he managed to escape into the new world. While there are hints that he ruled Ulgu before the god formerly known as Malekith rose to power, Be'lakor's first appearance had him get his ass royally handed to him by the Lizardmen dive bombing him with Pterodactyl riders. Embarrassed by this poor showing, he has since taken into hiding from the spotlight once more. That said, Archaon seems to be following his footsteps, as Archie's been elevated to the "High Marshal of Chaos", which gives him almost free reign to control or kill the champions of Chaos while still claiming no exclusive loyalty to any of the four (now five with the Horned Rat's ascension) - the only difference being that he's still arguably human. In Wrath of the Everchosen, it's revealed he's the Starscream to Archaon's Megatron, forming his own faction of Chaos followers with the (kinda-secret) goal of (eventually) overthrowing Archaon. Despite that, Bea'lakor worked with Archaon to defend the Eightpoints against the armies of Nagash, managing to personally slay the Mortarch Lady Olynder (As much as one can slay a Mortarch), sending her soul back to Shyish.
He's also got some big plans brewing, as he's got a new model incoming and is the star of the next Broken Realms book after Teclis'.
In Warhammer 40,000, Be'lakor was the first Daemon Prince, as well as the first (and allegedly "last", but there have been plenty more since) Daemon Prince created through the action of all four Chaos Gods (apparently Lorgar and Perturabo were special exceptions or something (though knowing Pert, I wouldn't be surprised if he was 75% Khornate or something and 0% Slaanesh considering what the Emperor's Cunts wanted to do with Pert)), and quickly proved to be difficult to control even at the best of times. Apparently his creation gave him the Daemonic equivalent of daddy issues and now he spends most of his time trying to kill all other Champions of Chaos, including other Daemon Princes. The Chaos Gods tolerate him mostly because his wild-card status makes him an excellent pawn in their power struggles, something Be'lakor himself is completely unaware of (as he thinks he still has free will and just wants to cement his position as Chaos' sole champion).
Recently, he's shown up to "help" with Abaddon's Black Crusades by giving him seemingly helpful advice that often leads to unexpectedly heavy losses, all in an attempt to undermine his credibility (well, more so than he does on his own). In a stunning display of insight, Abaddon saw through his ruse, but allowed him to remain within the Black Legion in order to keep tabs on him and better prepare for his sudden but inevitable betrayal. The Imperium isn't even that aware that he exists, as Be'lakor has been very careful about concealing his presence from history (with the unwitting help of a Magos who learned just enough about him to know that he exists, but not enough to realize that he's a Daemon Prince).
He's also been shown to be in contact with Ahriman. No word on whether Ahriman has accepted his offer of being made his greatest champion in exchange for his service, however, but seeing as Ahzek rejects even Tzeentch's own offerings to be HIS chosen champion, still thinks he's independent of any god (despite having Tzeentch's mark on the tabletop), and actively tries to become the fifth Chaos god himself, it's a good bet he told Be'lakor to go fuck himself with someone else's force sword.
During Gathering Storm Be'lakor helped the Iron Warriors invade the Imperial Fists star fortress the Phalanx, attempting to upstage Abaddon by using it to attack Terra directly. The Imperial Fists turned the Phalanx's own weapons on the chaos-tainted regions, destroying them and killing most of the Iron Warriors, then the Legion of the Damned arrived. Be'lakor himself got his ass kicked by Tor Garadon (before he was even given a model!). This abject failure was unfortunately the only time Be'lakor was ever really relevant to Warhammer 40k's plot. In general Be'lakor never really is shown doing much and seems to only exist in 40k because daemons in both settings have to cross-over.
A 500pt Monster (literally), Be'lakor is a very expensive but very solid choice for either a Warriors of Chaos or Daemons of Chaos army. He's an upgraded winged Daemon prince with Lore Master in the Lore of Shadow and a 4+ Ward save and any thing shooting at him suffers -2 to hit him to keep him out of the way of any cannons aimed at him. He is very good at making units run for the hills as he has Terror and Unbreakable like a regular Daemon prince but he also reduces the leadership of all enemy units with 12" of him by -1 and if they fail a panic or break test Be'lakor gets an extra D3 power dice for his next magic phase. Finally his sword, The Blade of Shadows is the standard but extremely nasty no armour saves allowed against wounds dealt by it. Over all if you use Be'lakor he'll take up your entire lord slot (unless you play using the last 8th edition FAQ and/or End Times in which case he uses half of it) but he can be very effective at scaring off hordes of enemies will pile driving your opponents lords while also being quite hard to pick off from usual monster killing methods, like artillery.
Age of Sigmar
Be'lakor's combat capabilities aren't really anything special. Sure, his melee capabilities are slightly better than your standard Daemon Prince, and ignoring rend is a neat gimmick (even if its offset by him having a lower save than the standard Daemon Prince. meaning its only really an advantage against Rend -2 weapons). He also heals himself when enemy models flee, but with battleshock being so easy to ignore its not much to speak about. His magic capabilities are better, having a good warscroll spell and being one of the few wizards that can cast twice in Slaves to Darkness. The real thing that makes Be'lakor a good pick, however, is his special rule "The Dark Master".
Be'lakor can secretly pick one unit at the start of the game, which he has secretly been manipulating the entire time. At any time he can reveal his manipulations, causing the selected unit to be unable to cast spells, move, charge, or attack unless they roll a 5+ for the rest of the turn. And of course, you're going to use this ability on the enemy's strongest unit. Need that Frostlord on Stonehorn to kill that one unit on the objective? Need Nagash to cast that combo of spells you need? Too bad.
Be'lakor also has his own subfaction for the Legion of Chaos Ascendant army list called The Legion of the First Prince. It allows lesser daemons to act as meat shields for him and also allows him to reroll hits and wounds if he's surrounded by at least one lesser daemon of each god, but you mainly take it for the command ability which allows him to restore dead models to every Plaguebearer, Bloodletter, Daemonette and Horror unit on the battlefield. Which, due to the way keywords work, include big multi-wound cavalry units like Bloodcrushers and Plague Drones.
His 40k rules are a reworked version of his Fantasy rules which were then super charged. A winged Daemon Prince he has a 4++ invuln save and is Shrouded, and he also has fucking Eternal Warrior so he's pretty hard to kill. The Blade of Shadows is in it's best incarnation as it's a monstrous S+1, AP2, Fleshbane, Armourbane, Master crafted murder stick, he is also a level 3 Psyker with powers from the Telepathy Discipline and he gains a bonus D3 warp charge points when enemy units fail moral tests. For 350 points he's expensive but he's a god damn steal with how killy he can be.
Be'lakor is pretty good in 8th edition. He's very speedy with a 14" movement and gives buffs to all Daemons so works round the restrictions of a regular Daemon prince. He has a -1 leadership debuff and he has 6 attacks. Stack that with his S+1 ap-5 D3 kill sword, he can carve his way through pretty much anything. He also has access to the Dark Heretics discipline which he knows 2 powers from (you will take Death Hex and you will like it) so he is a pretty good all rounder. The only problem is that he needs to be put in his own detachment as he doesn't have any marks of chaos (for some reason) so he can't join a god specific detachment without gimping the rest of the detachment.
Total Warhammer 3
It is implied that Be'lakor is going to be in Game 3 representing the Daemons of Chaos Undivided, considering that the existence of nine legendary lords was confirmed - 4 of them will probably be for Kislev and Cathay, another 4 will represent Chaos Gods, and the other one is currently unknown, but come on. "A shadowy source of great evil building its armies" has Be'lakors self stroking ego written all over it.
As he will (most likely) lead the Undivided Subfaction (if it will be in the game), he will presumably have access to all Daemons from 4.5 (included the few Undivided Daemons) rosters.