Mechanics: Illusions

There seems to be a lot of confusion around Illusions. I'd like to do a Discussion / Q&A to clear a lot of that up.

Basic Idea

• Illusions are meant to confuse the enemy, deal extra damage, etc.
• They have offensive and defensive/evasive uses
• They are imperfect (usually take more damage, deal less damage)

General Information

Illusions benefit from:

• Evasion
• Movement Speed bonuses
• Attributes (INT, AGI, and STR)
• Health and Mana
• Radiance's Burn Damage (does not stack though)
• Bonus Damage to Creeps from Quelling Blade

Illusions DO NOT benefit from:

• Raw Damage, Armor, or Attack Speed Bonuses (e.g. Items that say +50 Damage, +5 Armor, +15 Attack Speed, etc...)
• Magic Resistance from Items

Miscellaneous:

• If the hero levels up, the Illusions' level DO NOT chang
• Illusions have no regeneration. This is one way to check for the real hero

Common Misconceptions

NOTE: This is the CORRECT information for things people commonly say otherwise

• Illusions DO NOT benefit from any form of HP/MP regen, including Lifesteal
• Just because the Illusion plays the animation does not mean the effect is applied (remember, Illusions are used to confuse enemies. If an animation didn't play, it would be pretty obvious which one was real)
• ONLY Melee Illusions can benefit from Feedback (AKA Mana Burn)
• Riki's Illusions do not do bonus damage from Backstab (even if it appears as though they are)
• Illusions CANNOT Bash
• Illusions CANNOT Cleave (AKA Splash Damage)
• Illusions DO NOT benefit from Damage Block (i.e. Vanguard, Poor Man's Shield)
• Illusions CANNOT use most Unique Attack Modifiers (e.g. Lifesteal, Desolator, Eye of Skadi, etc..) though the animation will play
• Illusions CANNOT use Greater/Lesser Maim (e.g. Sange, Heaven's Halberd, etc..)
• Illusions can Crit, but they will deal less damage than the number that shows above their head (i.e. most Illusions deal reduced damage, but to hide the original, it will appear as though they Crit for the amount the original would have)

Niche Information/Little Known Facts

• Illusions benefit from True Sight (reveals invisible units), this means they reveal around themselves if the original had True Sight (i.e. like a Gem that doesn't drop when the holder is killed)
• Axe's Illusions inherit Counter-Helix
• Illusions inherit Magic Resistance from Abilities (but, as mentioned above, not from Items)
• Invoker's Illusions DO NOT display orbs (i.e. Quas, Wex, Exort
• If Templar Assassin's Psi Blades spill from an Illusion to another unit, the other unit will take amplified damage correlating to the bonus damage the Illusion takes (e.g. TA hits an Illusion for 100 damage, Illusion takes 300% amplified damge, Psi Blades spill for stupid damage)
• Luna's Illusions inherit Moon Glaive
• Manta Style provides an invisible Attack Speed Aura that Illusions benefit from (only applies to Hero + their Illusions)
• Spectre's Illusions benefit from Desolate
• Phantom Lancer's Illusions will play the Spirit Lance animation when the hero uses it

Auras

• Illusions will grant allies the auras that the original possesses
• Illusions will generally NOT benefit from the aura (EXCEPT for Attack Speed or Move Speed)

Bonus Damage to Illusions

Bonus Damage to Illusions:

• Outworld Destroyer's Arcane Orb
• Brewmaster's Storm Panda's Dispel

Instantly Destroy Illusions:

• Purge
• Hex
• Mana Drain (after 0.25 seconds) 
• Disruptor's Glimpse 
• Pugna's Ultimate

Special Illusions

• Morphling's Ultimate - Morph can swap places with it, appears as the color of the copied player
  Darkseer's Ultimate - Appear Blue to Enemies

References:
DotA 2 Wiki Referencial Data
Play DotA Mechanic Page