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 normally capped at 75%. However, there are passives and items that can increase your maximum resistances to allow for values higher than 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.
Basic burning effects last 4 seconds, and the amount of damage over time is 1/3 of the initial fire damage dealt, per second. So a total of 4/3 of the original damage, over 4 seconds. Total burning damage can be increased with skill gem bonuses, passive skills, and item mods that increase burning damage. In addition, the Vulnerability curse can increase burning damage, and the Temporal Chains curse can increase the duration of the burning effect without reducing the damage done per second.
Separate applications of burning damage do not strictly stack. All burning effects applied will be present on an enemy, but only the burning effect with the highest health degeneration value will take place at any given time. For example, if you apply a burning effect that damages an enemy for 10 health a second, and then one second later apply another burning effect that does 7 health each second, the enemy will burn for 10 health per second for the first 10 seconds. Then that burn effect will end and the 7 damage per second effect will apply for one second before expiring.
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.
Enemies killed while frozen will automatically shatter, leaving no useable corpse and ending any status ailments on the corpse (which is important for Elemental Proliferation). Chilled enemies also have a chance to shatter.
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% more damage per instance of Shock from all sources. Under the effects of 3 stacks of shocked, an enemy would take 220% of the damage that would normally be done without any shocked stacking, no matter the type or source of the damage.
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. Bonuses to Chill, Freeze, and Shocked duration can also be granted by skills and support gems, passive skills, and item mods. Temporal Chains will also increase the duration of all status ailments.
Status Ailments can also be triggered by skills such as Glacial Hammer, Burning Arrow, Chance to Ignite, and Elemental Weakness. When skills such as these trigger Status Ailments, the amount of relevant damage done is used just as it would be in the case of a critical hit. Because critical hits tend to do more damage than normal hits that can trigger a Status Ailment, the effects of a non-critical status ailment are often less severe. But such effects can still be quite powerful if the relevant damage type is very high.
If the duration based on the damage would be less that 300ms, it's ignored entirely. The only exception is burning, which will still take place no matter the amount of fire damage done.
Converted Damage
There are many skills, supports, and item mods which will convert one type of damage into another. Converted damage gains bonuses from both the type of damage it was converted from AND the type of damage it is converted to. The following is an example taken from the Path of Exile forums.
Mark_GGG wrote: I have glacial hammer converting 50% of my physical damage to cold damage, and Cold to Fire converting 50% of my cold damage to fire damage. Lets say my weapon deals 100 physical damage (in actuality there'll be two numbers, an minimum and a maximum, but we only need to do the maths once for the example, it's applied exactly the same to both).
I have: 10% Increased Physical Damage, 20% Increased Elemental Damage, 5% Increased Cold Damage, 15% Increased Fire Damage,
My weapon's base damage is 100 physical. 50% of this will be converted to cold, 50% of that (25% of the total) will be converted again to fire.
The physical damage will be affected only by the physical damage increase, for a 10% increase.
The cold damage will be affected by physical, elemental and cold increases, for a total 35% increase (10 + 20 + 5).
The fire damage is affected by physical, elemental, cold and fire increases, for a total 50% increase (10 + 20 + 5 + 15).
Physical:
50 of the base damage ends up being physical, with a 10% increase applied = 55 Physical Damage
Cold: 25 of the base damage ends up being cold, with a 35% increase applied = 34 Cold Damage (33.75 rounds up)
Fire: 25 of the base damage ends up being fire, with a 50% increase applied = 38 Fire Damage (37.5 rounds up)