This spell deserves its own chapter, as it requires a different way of playing. Let me provide the details on it first;
Enslave Demon
Enslaves the target demon, forcing it to do your bidding. While Enslaved, the demon’s attack speed and casting speed is lowered 30%. Lasts up to 5 minutes.
Repeatedly enslaving the same demon lowers the max duration of the spell.

*Important: As you level, the level cap of Enslave Demon increases with you. Rank 1 Enslave Demon actually lets you enslave up to a level 45 demon if you are 60.
Rank 2 lets you enslave up to 59, and Rank 3 goes up to 74 at level 70. Using a lower rank could save a little mana sometimes, but it doesn't make much of a difference.

Basics
The first and most important thing to remember when using enslave demon is that it is going to wear off either after 5 minutes, or earlier. To monitor enslave duration, you can download an Addon that keeps track of it, like Dotimer
(http://www.wowinterface.com/downloads/info5302-DoTimer.html).
Unsummon your pet before trying to enslave something, or the spell will fail. For safest usage, enslave only demons of at most 2 levels above you. Its safer to enslave at or below your level. To maximize the chance that the spell will stick to the target, open with Curse of Shadow (If you’re actually high enough to have that curse). The demon will come running toward you, and is bound to get off a hit or two before you can finish casting enslave. If you have a very low hp pool or the demon has an ability that interferes with spellcasting, you could also fear the demon first and then curse and enslave it. Stamina gear helps. Having a bigger hp pool increases your survival changes when that elite demon you enslaved breaks free in the middle of a fight. Enslave cannot be dispelled by others.
Keep a healthy amount of soulshards with you, enslave uses up a lot of them over time.
The Suppression talent helps you land enslave.
Infernal
The spell to summon Infernal is gotten through a quest in Felwood at level 50. See the walkthrough. The grimoire itself can be used at level 50 and is bind on pickup. The spell has a 1 hour cooldown, requires a reagent, (Infernal stone, costs 50 silver, can be bought from reagent vendors) and can only be cast outdoors. Casting it will make your regular pet disappear, and makes the infernal appear in enslaved status for a guaranteed 5 minutes. He acts as a regular enslaved demon, meaning you will have to re-enslave him when it breaks after those first 5 minutes. Cast Curse of Shadow before enslaving to increase the chances of enslave lasting full duration. The Infernal is a pure melee pet, and puts out fairly good damage, about 130-230 each hit at level 60 up to 515-620 at level 70. He has an AE that burns nearby enemies for 35 damage every 3 seconds. You can’t turn this off, so that can be a problem if you have anyone trying to crowd control nearby.

Doomguard
There are two spells to summon this guy. One is Curse of Doom, acquired at level 60 from your warlock trainer. The curse does nothing for 1 minute, and then deals 3200 damage. If the target dies from that damage, there is a small chance that a doomguard will appear. I’m not sure of the percentage chance here, but it probably lies around 10-20%. It can be quite a hassle trying to make him appear this way. The second spell is Ritual of Doom, which can be gotten through a quest in the Blasted Lands at level 60. See the walkthrough.
You can cast Ritual of Doom once an hour, and it uses a Demonic figurine as reagent. (costs 1g at reagent vendors) The ritual requires 4 helpers to assist. When the ritual completes, one of the 5 people participating in this ritual (so that includes the warlock) will be randomly selected to die. After that, the Doomguard will appear. Whoever dies can be resurrected right after. This does not cause a durability loss.
The Doomguard has some pretty cool abilities. For one, he can cast Rain of fire, and it cannot be interrupted or shortened by melee attacks like our own can. Secondly, he has an ability called Cripple, which will severely reduce the targets movement and attack speed. He also has an ability similar to the Felhunters Devour, and a small AE that stuns enemies for 2 seconds. Lastly, he does a fair amount of melee damage, though not really impressive. 150-200 per hit at 60, 570-680 at 70. He doesn’t have too much health.

What Enslave Works With
Back in the old days, Enslave did not work with most Demonology talents. Soul Link used to work, and that got nerfed.
Luckily, blizzard decided to reverse that decision and made a few talents work an enslaved demon.
Soul Link once again works with an enslaved demon out, as does Demonic Knowledge.
The amount of spell damage gained through Demonic Knowledge with a regular summoned pet at level 70 will generally be above 100. You will have a smaller return with an enslaved demon, somewhere around 50-60. The reason for this is that mobs in wow tend to have relatively low base statistics, which in turn reduces what you get out of the DK talent. Secondly, pet scaling is not in effect with enslaved demons, which takes another bite out of the DK returns.
Even so, its better than the way things used to be, which was having only one talent function with Enslaved Demon. (Improved Enslave Demon)

Listing Of Enslavable Demons
Sadly, the majority of the demons you will find out and about in WoW are not worth enslaving. They either do less damage than your pet or only slightly more, which doesn’t outweigh the downsides to enslave. But, since some are and because it can be fun to just enslave something to have a different pet for a change, here’s a list of what demons you can get where:
Azeroth

Outland

Outland Instances

Groups And Enslaving
Enslaving a demon can help greatly in effectively CC'ing two targets (one will be under your control, and you can make it attack an add), as well as being a good source of damage.
Make sure to communicate with your group about enslave. Let them know you're planning to use it. Especially let them know if you're going to let one loose you'd like to see killed.
Enslaving Elites And Demons Above Your Level
If you enslave a level 54 elite infernal in Felwood while you are 52, expect to have a little fun watching it lay waste to enemies, but also expect to get killed at any time. Enslaving enemies above your level (especially elites) is extra risky because they have a higher chance to break free early. Curse of Shadow helps, but doesn't overcome level differences.