Imbue

In Update 57, several existing abilities that granted extra damage, usually on weapon hits, were consolidated into the imbue system.
 * Characters can gain imbues from various sources.
 * Imbues are toggles: You have to drag them to a hotbar and enable to become active.
 * Only one imbue can be active at a time.
 * Various effects that were originally used to increase the damage of a particular imbue system are streamlined and grant extra imbue dice. Extra imbue dice from various sources stack. You can check your bonus Imbue Dice on the character sheet's Details+ Tab
 * Your imbue damage is multiplied by Doublestrike and Doubleshot.

Extra dice
Alchemist:
 * Vile Chemist Core 2: +1 Dice at Alchemist levels 6, 9, 12, 15, and 18 - Max 5 (seems to also grant an undocumented +1 die when you take the ability as Alchemist 3)
 * Vile Chemist Core 4: +1 Dice
 * Vile Chemist Core 5: +1 Dice
 * Vile Chemist Core 6: +2 Dice

Artificer:
 * Battle Engineer - Agility Engine t4: +1/2/3 Dice with a runearm equipped
 * Battle Engineer - Unlock Potential t5: +1 Dice with a runearm equipped

Barbarian:
 * Frenzied Berserker Core 5: +3 dice while Death Frenzy is active

Bard:
 * Swashbuckler Music Box: +1 Dice
 * Warchanter: Each core beyond the first grants +1 Dice

Cleric:
 * Warpriest: Core 2, 4, 5 grant +1 Dice
 * Warpriest T5: Wrathful Weapons: +3 dice, change Fire imbue to Light for the duration
 * Dark Apostate: Tiers 2, 3, 4 grant +1 Dice
 * Dark Apostate: Tier 5 grants +2 Dice
 * Dark Apostate: Core 3, 5, 6 grant +1 Dice

Druid:
 * While wild-shaped into a Fire or Water Elemental, gain +3 Dice (requires druid 13) (Having access to both elemental forms (druid 17) does not increase the number of dice.)

Favored Soul:
 * Warsoul: Cores 2, 4, 5 grant +1 Dice
 * Warsoul T5: Wrathful Weapons now grants +3 dice instead of its separate proc, and turns your Fire imbue to Light for the duration

Monk:
 * Henshin Mystic: Each core grants +1 Dice

Paladin:
 * Sacred Fist: Each core beyond the first grants +1 Dice
 * Sacred Fist: Tier 3, 4 grant +1 Dice each
 * Knight of the Chalice: Each core beyond the first grants +1 Dice

Ranger:
 * Arcane Archer: Tiers 2, 3, 4, and 5 grant +2 Dice each. (Note: All other primary Arcane Archer imbues are also now imbues in this system.)

Rogue:
 * Assassin - Tier 2: Toxin Affinity: +1/2/3 dice

Sorcerer:
 * Eldritch Knight Core 2: +1 Dice at Sorcerer levels 6, 9, 12, 15 and 18 for a total of 5 dice
 * Eldritch Knight Core 4: +1 Dice
 * Eldritch Knight Core 5: +1 Dice
 * Eldritch Knight Core 6: +2 Dice + the proc for +4 temporary dice

Wizard:
 * Eldritch Knight Core 2: +1 Dice at 3 Wizard levels 6, 9, 12, 15 and 18 for a total of 5 dice
 * Eldritch Knight Core 4: +1 Dice
 * Eldritch Knight Core 5: +1 Dice
 * Eldritch Knight Core 6: +2 Dice + the proc for +4 temporary dice

Warlock:
 * Enlightened Spirit Core 5: +3 bonus dice while in Celestial Spirit form

Racial:
 * Drow - Racial Tree: +1 dice in tier 3, 4: new enhancements, fills in missing space

Universal:
 * Inquisitive: Core 4, 5, 6 grant +1 dice each
 * Inquisitive: Tier 2, 4 grant +1 dice each
 * Inquisitive: Tier 5 multi-selector grants +1 dice each except for 1 grants +2

Spells

 * Elemental Weapons: +1 alchemical bonus
 * Greater Elemental Weapons: +2 alchemical bonus
 * Sacred Fist Empowerment: +3 imbue dice and your critical hits deal 1d20 Bane damage per Imbue dice, scaling with 100% of your Melee Power.

Feats

 * Embodiment of Law - Destiny Feat: +2 Dice if lawful
 * Harbinger of Chaos - Destiny Feat: +2 Dice if chaotic
 * Enhanced Elemental Dice - Destiny Feat: +1 Dice
 * Scion of Arborea - Legendary Feat: +1 Dice
 * Scion of the Feywild - Legendary Feat: +3 Dice
 * Scion of the Plane of Earth - Legendary Feat: +3 Dice
 * Scion of the Plane of Fire - Legendary Feat: +3 Dice
 * Scion of the Plane of Water - Legendary Feat: +3 Dice
 * Scion of the Plane of Air - Legendary Feat: +3 Dice
 * Offhand Versatility - Orb/Runearm: +1 Imbue dice

Destinies

 * Shiradi Champion mantle gains 1d77 per 7 bonus dice - this is not an imbue toggle BUT gains benefits from your imbue dice!
 * Draconic Tier 3 now grants +1/2/3 Dice
 * The Crusade! buff in Divine Crusader now grants +1 dice
 * Ghost Touch in Legendary Dreadnought is now "Esoteric Touch" and grants both Ghost Touch and +1 Imbue Dice
 * Shared Mantle in Primal Avatar now also grants +3 Imbue Dice while within the PA Mantle

Items

 * Filigree Set Bonuses that used to give a scaling imbue on-hit now give +1/+2 Dice
 * Augments from Hunt or Be Hunted Raid now give +1 Enhancement bonus to bonus Dice
 * Certain Set Bonuses get +1 Dice in heroics, 2 in epics, 3 in legendary (artifact typed):
 * Profane Experiment
 * Echoes of the Waking Ancestors
 * Crypt Raider