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Glancing
Glancing blows are combat events that can occur when fighting a mob of equal or higher level.
These occur only on white damage, cannot crit, and result in the attack having it's damage reduced in proportion to the difference between the attacker's weapon skill (capped at the attacker's level * 5), and the target's defense skill.
At current Glancing blows occur at about 30% of the time versus mobs that are above your level. These attacks only do 70% of their normal damage versus a mob that is 3 levels above you. (10% per mob level). Bosses are counted as "your level+3".
Effect from Weapon skill
Weapon skill greater than the normal max for your level (i.e. your level * 5) does not reduce the chance for a glancing blow to land.
 Prior to 2.0.1, extra weapon skill did reduce the severity of the damage reduction, but this is no longer the case.
Glancing blows do not occur against players, only against mobs. At present ranged attacks do not result in glancing blows.
Glancing blows
Against mobs with defense roughly equal to or higher than your Attack Rating (i.e. your weapon skill), you will have a chance to land a glancing blow instead of a normal hit. A glancing blow only occurs on white melee damage, cannot crit, and does less damage than a normal blow. If the attacker's weapon skill is less than his level * 5, the damage reduction will be proportional to the difference between the attacker's weapon skill and the target's defense. Weapon skill above your level * 5, as from gear or racial bonuses, affects neither the damage reduction nor the chances of landing a glancing blow.
Glancing Blow chance
Pre 2.1
Players have a chance to perform a glancing blow against mobs equal to 10% plus 2% per point of difference between attack rating and defense. Nonmelee classes level 30 and higher have a 60% chance to glancing blow. Nonmelee classes from level 11 to level 29 have a (level  10) * 3% chance of a glancing blow. As noted above, your maximum attack rating in this formula is 5 times your level. A mob's Defense skill is equal to its level * 5.
This formula means that, for a level 60 player with fully trained weapon skill, 30% of all whitedamage melee attacks will be Glancing Blows against level 62 mobs, and 40% of all whitedamage melee attacks will be Glancing Blows against level 63 mobs.
The presence of your weapon skill in this formula, rather than just your level, explains why training up a newlyacquired weapon skill against mobs close to your own level results in many, many Glancing Blows at first.
Post 2.1
The release notes for patch 2.1 say the following:
 Glancing Blows have significantly less of a chance to occur during a player's melee attacks when targets are near the player's level.
Glancing Blow damage reduction
The damage of a glancing blow is complicated. It starts by calculating the difference between the target's Defense and the attacker's attack rating, where the attack rating is capped at the attacker's level * 5 (just as it is for determining the chance of a glancing blow occurring). This is then used to calculate a minimum and maximum damage factor. The actual damage factor is then randomized between these two values. The low value starts at 1.3  0.05 * rating difference. If the attacker is a caster then this is reduced by 0.7 more. The smaller value of this and 0.6 is kept as the low end. If the attacker is a melee class then instead the lower value of 0.91 and (1.3  0.05 * rating difference) is used for the low. Regardless, the low end will not go below 0.01.
The high end of the range starts at 1.2  0.03 * rating difference. Casters are reduced a further 0.3. The high value regardless of class is kept between 0.2 and 0.99.
The average reduction from a glancing blow is therefore (high + low) / 2 using the formulae above. This gives a level 60 player, with a weapon skill of 300 or more, a 15% damage reduction with all Glancing Blows against level 62 mobs, and a 35% damage reduction with all Glancing Blows against level 63 mobs.
As of 2.0.1, the player's weapon skill is capped at level * 5 in the damage reduction formula, just like it is in the formula for determining the chance of a glancing blow. (Before 2.0.1, glancing blows landed against a level 63 NPC by a level 60 player with +10 Weapon Skill would do nearly as much damage as the player's ordinary hits did.)
Glancing Blow Implications
The fact that 40% of all whitedamage melee attacks made against a Boss Mob will be Glancing Blows, no matter what you do, has serious implications when choosing how much +crit% gear to use. Due to the tablebased nature of WoW's attack resolution system, Glancing Blows take precedence over critical hits. If your combined miss, dodge, parry, block, glancing blow, and crit chance against a mob is 100% or higher, you will never see a normal whitedamage hit made against that mob (all your hits will be either glancing blows or critical hits). If it exceeds 100%, it is your critical hit chance that gets "pushed off the end" of the table. Any +crit% gear added past this point will not improve your critical hit chance with whitedamage melee attacks at all. This is sometimes called the "Crit cap" (see below).
Instant attacks, and "yellow damage" onnextswing attacks such as Heroic Strike, do not produce Glancing Blows. For these attacks, added +crit% gear beyond the "Crit cap" described above will improve your critical hit chance.
Ranged weapon attacks (Bows, guns and crossbows) do not have glancing blows at all, thus weapon skill does not affect this for them. It works the same for all classes that can use ranged weapons (hunters, rogues and warriors).
Notes
There is still a debate on how to determine the chance of a glancing blow occuring, and it's severity. (see Talk page).
 See also: Formulas:Weapon_Skill#Glancing_blows