Damage
There are currently 5 main types of damage, they are Physical, Fire, Cold, Lightning, and Chaos. Fire, Cold, and Lightning are collectively known as Elemental Damage. Damage reduction from armour only affects physical damage. Each of the elemental damage types has it's own resistance value (eg "Fire resistance") which is viewable in the character sheet. Resistances reduce damage taken, and are capped at 75%.
Fire damage
If you land a critical strike with an attack or spell that deals fire damage, the enemy begins Burning. Burning causes damage over time. Humanoids, Monkeys and Sea Witches will flee while burning.
Burning lasts 4 seconds, and the amount of damage over time is 1/3 of the fire damage dealt per second. So a total of 4/3 of the original damage, over 4 seconds.
Cold damage
Hitting an enemy with cold damage can cause the enemy to be Chilled. Critical hits with cold damage can also cause the target to be Frozen. Chilled enemies move, attack, and cast 30% slower, while frozen enemies cannot do anything except drink flasks.
Lightning damage
If you land a critical strike with an attack or spell that deals lightning damage, the enemy becomes Shocked. This can be stacked up to three times on one target. In this state, monsters or players take 40% additional damage per instance of Shock.
Chaos Damage
Chaos damage ignores energy shield, reducing life directly.
Status Ailments
Burning, Chilled, Frozen, and Shocked are collectively known as Status Ailments.
The duration of the chilled, frozen, and shocked statuses is related to the amount of cold/lightning damage dealt.
If the duration based on the damage would be less that 300ms, it's ignored entirely.