There is limitation of three special units, or four special units in armies of 2000 points or more. The special infantry choices described here will be competing with war machines for one of these three or four slots. Its worth remembering that Longbeards are an elite warrior unit but only take up a core slot.
The models: You get 8 plastic miners in the Battle for Skull Pass box set. You can also get box sets of 10 or 20 plastic miners.
Miners are an interesting unit. For only 1 point more than Warriors with great weapons and no shields, you get the same stat line but have the Underground Advance special rule. This means that you can either deploy your miners normally or have them come on from reserve from any board edge. As such they are often used to attack enemy war machines or to disrupt enemy attacks moving up the flanks by either attacking the units or my march blocking. They could also be used to claim or contest table quarters later in the game.
You can also try and use Miners for march blocking. Recall that units can only march if there are no enemy models within 8" of them at the start of their move. However, Dwarfs have the Relentless rule, and so your miners can march even if there are enemy within 8". If you can get in behind or on the flank of one or more enemy units then you should be able to keep up with them and slow their movement for several turns, or they will have to waste two or three turns dealing with your unit.
You should remember that in the movement phase that you come on to the board that you can only move 3", and you cannot charge. With a 5+ save, miners are quite vulnerable to shooting. Thus they are more useful in threatening a unit that cannot shoot you (eg stone thrower or a unit facing the wrong way with hand guns or crossbows) when you first move on rather than something that can shoot you (repeater/reaper bolt thrower, cannon or organ gun) or shoot after moving (bows and repeater crossbows).
The situation changes in games of 2000 points or more if you have the Anvil of Doom. With the Anvil of Doom the miners can move on 3" in their movement phase and then charge 6" in the shooting phase.
If you don't have an Anvil of Doom, use small, cheap units of 5 - 8 Miners. This means that the miner unit is worth less than the war machine it is sent to attack or the table quarter it is sent to claim, so you stand to gain more points than you are putting at risk. With such a small unit you might want a musician to help with rally tests, though if you fail a panic test only 3" from the board edge the chances are that you will have run off the board. A standard bearer is not a good idea.
If you have an Anvil of Doom, then you have a good chance of being able to charge any enemy unit within 9" of a board edge. It may be worth having larger miner units, or even having two units of miners. If you use two miner units, provide one with a prospector with a steam drill. When rolling for your reserves, you probably only want one miner unit to come on per turn (as the Anvil of Doom can only reliably allow one unit to move during the shooting phase) so roll for the unit with the steam drill last.
The models: Box sets of 5 metal models are available. Depending on your modelling skills you could convert plastic warriors or miners into Hammerers. Check out the Bugman's Brewery topic on making hammerers from plastic models.
Hammerers are elite fighters (with the same stat line as Longbeards) armed with great weapons. The most important thing about them is that they are Stubborn. If they lose a battle you will only need to roll 9 or less to pass the break test, regardless of how much they lost by. Even if they are charged in the flank or rear, they should still hold their ground. As such they make a good unit for guarding your flanks of your army.
A unit of at least 10 Hammerers should be able to survive a charge from most single enemy units. Always give the Hammerers shields so you have the extra protection against shooting and the option of either being S4 with a 3+ save or S6 with a 5+ save in close combat. In most cases you will end up choosing to use the hand weapon and shield option in close combat rather than the great weapon.
A unit of 15 to 20 Hammerers with full command (gatekeeper, musician and standard bearer) and a runic standard would be the preferred unit size in games of 2000+ points.
If the unit loses a combat against a fear causing enemy that outnumbers them, then Stubborn doesn't help them and they will need to roll Insane Courage (double one) to stay in the fight. When a Dwarf Lord is in the unit they then become immune to fear and terror, and so keep the benefit of their Stubborn rule. If you are not using a Dwarf Lord, then consider giving the unit a runic standard with the Rune of Courage to make them immune to fear and terror
You can also give the Hammerers the Rune of Determination and they can take a single break test (ie roll 9 or less) on D6 rather than 2D6 so that they're effectively unbreakable for one break test.
The models: Box sets of 5 metal models are available. Depending on your modelling skills you could convert plastic warriors into Iron Breakers.
Iron Breakers are elite fighters with the best armour save of any infantry unit in the game, with a 2+ save in close combat against attacks from the front and a 3+ save against flank/rear attacks and shooting.
Iron Breakers are the same points as Hammerers with shields. Many players will choose between a unit of Iron Breakers or a unit of Hammerers for their army. Iron Breakers are probably better against opponents that are mainly infantry armies with S3 or S4 weapons. Against opponents with large numbers of elite knights with S5 or S6 attacks on the charge their armour save becomes 4+ or 5+ and the stubborn rule of the Hammerers would probably be more useful.
Iron Breakers will normally win combats more by static combat resolution rather than kills. As such you would want a unit of twenty models with full command. Because they will lose their rank bonus if charged in the flank or rear, and their armour save is "only" 3+ against flank or rear attacks, you will normally use Iron Breakers as the armoured spearhead of your battle lines. In this role their flanks should be protected by your other units and you are forcing the enemy to deal with your most heavily armoured unit.
Alternatively, consider adding a Thane or Lord with an Oath Stone. When the unit is charged the character can plant the Oath Stone and the unit then effectively has no flanks or rear. In this configuration the unit could even be used to anchor a flank. However, after the Oath Stone has been used the unit cannot move again for the rest of the game.
The models: Box sets of 5 metal models are available. There is also a single plastic slayer model in the Battle for Skull Pass.
Slayers are unbreakable and are often referred to as tar pits. The "tar pit" expression refers to the fact that any enemy unit that attacks them will not be able to break the unit, and will be bogged down for several turns while they try and kill the Slayers. Because of this, Slayers are often used to guard the flanks of your army.
Being unbreakable, Slayers are also Immune to Psychology. They thus don't have to worry about taking Panic, Fear or Terror tests. This makes them great when facing opponents such as Vampire Counts.
Unlike your other special units, such as Miners or Hammerers, an army may only normally include a single unit of Slayers (refer sidebar on p56 of Dwarf army book). If you want more than one unit of Slayers, you must add a Daemon Slayer or Dragon Slayer hero for each additional Slayer unit you want to add.
Adding at least one Giant Slayer to the unit means that you should normally get at least a few attacks back even if your opponent kills an entire rank of models each turn. Also the Giant Slayer can issue a challenge and so save the rest of the unit against a characters attacks.
The weakness of Slayers is that they have no armour, so they are vulnerable to shooting. Also as they are Immune to Psychology they cannot choose to flee as a charge reaction. But hey, they wanted a glorious death in battle, right?