Untargetable refers to champions in a state where targeted spells such as 
Rammus' 
Puncturing Taunt and 
LeBlanc's 
Sigil of Malice cannot be cast on the untargetable champion, and nontargeted spells such as 
Karthus' 
Requiem will have no effect; an exception being 
Soraka's 
Wish. Additionally, they cannot be targeted by auto attacks.
List
Game Removal
Shaco's Hallucinate completely removes him from the game for a short time before the clone spawns. (This can dodge everything, including aoe's, ignite ticks, and ability procs. Leashes continue attached to him after he clones)
Complete invulnerability
These break all forms of leashes and makes the champion untargetable and provides inmunity to all DoT effects (DoTs continue to deal damage once the invulnerability ends if they have not expired yet, they are not cleansed)
- Lissandra's Frozen Tomb makes her untargetable for 2.5 seconds if cast on herself.
- Zilean's makes a champion untargetable for 2 seconds before revival.
- Zhonya's Hourglass's active ability makes your champion untargetable for 2.5 seconds.
- Guardian Angel's passive makes your champion untargetable for (estimated) 3 seconds before revival.
- Aatrox's Blood Well makes him untargetable for 3 seconds while reviving.
- If a champion dies, they will be untargetable.
Partial invulnerability
Projectiles fired before the untargetability starts will have no effect. They will still take damage from DoTs such as 
Ignite and 
Malzahar's 
Malefic Visions and will not break leashes such as 
Fiddlesticks' 
Drain and 
Morgana's 
Soul Shackles. They will not be damaged by delayed abilites such as 
Zilean's 
Time Bomb and 
Fizz's 
Chum the Waters, but will be damaged by 
Vladimir's 
Hemoplague and 
Zed's 
Death Mark
- Fizz's Playful makes him untargetable for 0.75 seconds or until he uses Trickster.
- Vladimir's Sanguine Pool makes him untargetable for 2 seconds.
- Elise's Rappel makes her untargetable for 2 seconds or until it is recast on an enemy target.
Dashes
Projectiles (autoattacks or abilities) that are mid-flight when the character starts dashing will hit when the dash completes. They still take damage from DoTs while untargetable and all CC is delayed until the ability finishes casting.
- Maokai's Twisted Advance makes him untargetable while moving to the target.
- Zed's Death Mark makes him untargetable while moving to the target.
- Master Yi's Alpha Strike makes him untargetable for a short time while in flight.
- Fiora's Blade Waltz makes her untargetable for a short time while in flight.
Damage Invulnerability
- Kayle's Intervention grants the immunity to damage for the duration. DoTs that are still taking effect will continue their damage once Intervention ends, and the target can be affected by all forms of CC while it lasts. The unit can still be targeted by attacks and damaging abilities, but will not receive any damage from them.
- Poppy's Diplomatic Immunity will grant immunity to damage and CC from all sources other than her target. She can still be targeted by attacks and abilities from other sources, but will not take any damage from them, nor will she be affected by any CC from them.
- Tryndamere's Undying Rage will prevent any further damage when he hits 1 hitpoint, but he can still be targeted by attacks and abilities. All forms of CC will still affect him.
Note: The Nexus Obelisk ignores all Damage Invulnerability effects and can damage and kill any champion while the effect lasts. If a unit is untargetable, however, the Obelisk will not fire at it.