The "Refused Flank", or oblique order as it's also called, is a useful tactic when facing a numerically superior force. In this formation, you will intentionally weaken a portion of your line, concentrating the majority of your strength against one flank of the enemy, acheiving a local superiority in numbers.

This formation is ideal if you're deploying second against a numerically superior opponent. If you end up having to deploy first, you may need to place a few units along your line to bait your opponent into deploying across a broad front. Units deployed in this 'decoy' duty should ideally be able to redeploy fairly quickly. Tanks or other vehicles work best in this role.

At this point, you can either attack or hold your ground depending on whether or not you have the advantage in mobility. If you opt to attack, you hit one enemy flank with concentrated force, while "refusing" your weakened flank. If you hold tight, you will be forcing your opponent to approach piecemeal into the majority of your army rather then facing off with equal forces.

With either approach, aggressive or defensive, the idea is to defeat the enemy army in detail, killing a unit at a time and working your way up his line. Your units operate in close support of one another, while the enemy on the opposite flank is out of range.

The "Refused Flank" can be effective in Annihilation missions, but you will need to have a plan for capturing or contesting objectives that are away from your main force concentration.
 

The Refused Flank - Defensive

The "Hook" looks a lot like a phalanx deployment, at least until you start placing fast units. Deploy your heavies and troops in normal phalanx fashion, opposite the enemy across a fairly broad front. Then place your fast units to one side of your line, in a position to hit one of the enemy's flanks.

The basic premise is to "Steamroller" with your main line while your "hook" element speeds in and hitsa weak point in the enemy battle line. The flanking units attempt to roll-up his line and take out his 'CoG', while the rest of your army moves in to mop up.

This formation is great if you're going second. By looking at the enemy deployment, you can look for any weak spots in his line and place your fast units in a position to exploit it. If you end up deploying first, you will have to be sneaky about how you deploy your fast units. Space them out a bit, but ready to group up and hit the enemy when the time is right. If you are too obvious and line them all up on one side, you opponent will very likely see what you're up to and deploy his army to counter you.
 

The "Pincer", or double envelopment, is a classic element of military strategy which has been used to great effect throughout history. At first glance it appears very similar to the "Hook" attack, but there are a couple of differences.

The most notable difference between "Pincer" and the "Hook" is that both flanks of your opponent's army are attacked simultaneously instead of just one. Another more subtle difference is that your fixing force isn't used as aggressively in the "Pincer" attack. The center of your line either holds position or gives ground to lure the enemy in.

Hannibal's double envelopement of the Romans at the Battle of Cannae in 216 BC is viewed by military historians as one of the greatest battlefield maneuvers in history. It is cited as the first successful use of the pincer movement to be recorded in detail.
 

The "Bull's Horns" is similar to the pincer. It is an aggressive tactic pioneered by the Zulu of South Africa. The attacking force is divided into four groups - two in the front, one on the left, and one on the right.

The main group would face the enemy, while two "horns" would engage the enemy on either side and force them towards the center. The fourth party (usually the veterans) remained as a reserve.

Translating the "Bull's Horns" to 40k is pretty simple. It uses a deployment very similar to the pincer maneuver. Fast units deploy on either side to advance forward and encircle the enemy. The center of your line, instead of acting as a lure, like in the pincer, is now the main force behind your attack.