Damage modifiers refer to the buffs or debuffs to a unit that causes it to deal or receive increased or decreased damage. These are percentual values. They don't add extra flat damage but modify all damage normally done. These buffs or debuffs are only recevied by champion abilities, neutral buffs, on-hit effects from items and masteries.
Damage dealt modifier
These are buffs that allow the champion that has them to deal increased or decreased magic or physical damage from auttoattacks, abilities, item's actives and 
Ignite. The raw value from the attack or ability is increased or decreased by the modifier and then applied to the target.
All damage dealt modifiers stack multiplicatively. So if 
Talon uses an autoattack on a cc'd champion just after using a maxed 
Cutthroat on it, while affected by 
Urgot's 
Zaun-Touched Bolt Augmenter, his autoattack's damage will be modified by 107.525% (110%*115%*85%).
Champion abilities
Note: Only the damage modifier effect of these abilities is shown here, to read more information on each of these abilities, follow the link on each of them.
Kayle's Reckoning blasts her target and slows it for 4 seconds. While the target is slowed, Kayle inflicts 6 / 7 / 8 / 9 / 10 % more damage to the target from all sources.- Poppy's Diplomatic Immunity allows her to focus intensely on one single target for 6 / 7 / 8 seconds to deal 20 / 30 / 40 % increased damage to it from all sources.
- Shaco's Backstab allows him to deal 20 % increased damage when striking a unit from behind with his autoattacks or abilities.
- Swain's Torment afflicts his target, dealing damage to them over time and causing Swain to deal 8 / 11 / 14 / 17 / 20 % increased damage to it for 4 seconds from all damage dealt by swian(includes ignite smite and items).
- Talon's Mercy allows his autoattacks to deal 10 % increased damage if his target is slowed, stunned, immobilized or suppressed.
- Talon's Cutthroat allows him to blink to his target and deal 3 / 6 / 9 / 12 / 15 % increased damage to it for the next 3 seconds.
- Vladimir's Hemoplague infects all enemies in the target area with a virulent plague which increases the damage they take from all sources by 14% for 5 seconds.
Masteries
- Template:Mi increases your champion's physical and magical damage by 0.5/ 1 / 1.5 %.
- Template:Mi increases all damage dealt by your champion by 6 % to enemies under 40 % of their max health.
Decreasing damage dealt
Champion abilities
Note: Only the damage modifier effect of these abilities is shown here, to read more information on each of these abilities, follow the link on each of them.
- Sona's Aria of Perseverance enhances her Power Chord, to debuff her target to deal 20% less damage for 4 seconds.
- Urgot's Zaun-Touched Bolt Augmenter makes his autoattacks reduce all damage that his target deals by 15% for 2.5 seconds.
Damage received modifier
These are buffs or debuffs that allow the champion that have them to receive increased or decreased magic or physical damage from autoattacks, abilities, item's actives and Ignite. The final value from the attack or ability is increased or decreased by the modifier and then directly applied to the target's health.
Armor and magic resistance damage reduction percentage count as one source of damage received modifier against physical and magical damage respectively. For example, a champion with 300 armor has 75% damage reduction from physical damage.
Damage reduction from armor and magic resistance and from any other sources stack multiplicatively.
Increasing damage received
Note: Only the damage modifier effect of these abilities is shown here, to read more information on each of these abilities, follow the link on each of them.
Champion abilities
- Vladimir's Hemoplague affects all targets hit to receive 14 % increased damage from all sources for the next 5 seconds.
Decreasing damage received
Champion abilities
Note: Only the damage modifier effect of these abilities is shown here, to read more information on each of these abilities, follow the link on each of them.
- Alistar's Unbreakable Will grants him 50 / 60 / 70 % damage reduction for 7 seconds.
- Galio's grants him 50 % damage reduction while channeling for up to 2 seconds.
- Garen's Courage places a defensive shield on himself, decreasing all damage taken by a 20 / 24 / 28 / 32 / 36 % for 3 seconds.
- Gragas' Drunken Rage channels for 1 second and then receives 10 / 12 / 14 / 16 / 18 % reduced damage for 20 seconds.
- Kassadin's Void Stone reduces all magic damage taken by 15 %.
- Katarina's Killer Instincts enhances Katarina's Shunpo to grant her 15 / 20 / 25 / 30 / 35 % damage reduction for 3 seconds after blinking.
- Maokai's Vengeful Maelstrom creates a great vortex of natural energy on a nearby area reducing non-tower damage done to allied champions in the area by 20% until toggled off.
- Yorick's Unholy Covenant grants him 5 % damage reduction for each ghoul currently summoned.
Items
- Leviathan grants the wearer 15 % damage reduction when at 20 stacks.
- Ninja Tabi grants the wearer 10 % damage reduction from physical autoattacks.
Masteries
- Template:Mi reduces all damage taken (besides true damage) by 4%.