Invisibility

Invisible units and Heroes do not appear on their opponent's screen or minimap, and cannot be targeted directly. Invisibility makes the unit's model appear transparent, but clearly visible still for allies. If it's an allied hero, its dot on the minimap also turns into a ring for the duration. A unit can gain (usually temporarily, but not always) invisibilty through certain spells, items or the Rune of Invisibility. Some units, like most wards have permanent invisibility and don't need to acquire it through other sources. Generally, a unit remains the gained invisibility until the duration runs out, or they perform an attack or a spell or item cast. True Sight and shared vision allows a unit to see invisible enemies without dispelling the invisibility. True Sight makes the units appear transparent, while shared vision only shows a silhouette. Both make the unit directly targetable again, without dispelling the invisibility.

Fade Time and Fade Delay
Most sources of invisibility require some time to turn the unit fully invisibile. During this time, the unit is still visible and targetable.

The fade time is a short delay before the actual invisibility is applied, during which a unit's model will appear transparent, but still visible to everyone. During it, the unit will not automatically attack nearby enemies, no matter if auto-attack option is turned on or not. It also will stop attacking when an attack order was already ongoing. Unlike during the actual invisibility, during the fade time, the unit can cast spells or items and even attack without canceling the invisibility. It is safe to perform those actions during the fade time. During the fade time, the unit is not phased, even when the invisibility of the spell phases the unit.

The fade delay is also a short delay before the actual invisibility is applied, but has some significant differences. First off, during the fade delay, the unit's model will not appear transparent. The unit will also not stop automatically attacking nearby enemies when the auto-attack opton is turned on, and also will not cause the unit to cancel the already ongoing attack order. It is also not possible to cast spells or items or attack during the fade delay without resetting it. During the fade delay, the unit is not phased, even when the invisibility of the spell phases the unit.

Unit Behavior during Invisibility
While invisible, a unit will never automatically attack any nearby enemy, not even when it is revealed by True Sight and being attacked. However, when issuing an attack ground order, the invisible unit will attack. Generally, the invisibility is lost upon reaching the attack point. For ranged heroes, this is upon projectile launch. Depending on the source, invisibility may or may not apply a phase effect on the target.

As for spell casts, the invisibility is lost upon reaching the cast point of the spell. This means that spells with extended effects like or  will not cancel the invisibility upon each beam or pulse. Channeling spells will not cancel it either when going invisible after the channeling started.

All ranged attacks and most projectiles of abilities are disjointed by Invisibility. It is enough for a unit to turn fully invisible even just for a split second as a disjointable projectile flies to fully disjoint it. However, some projectile abilities will still affect invisible units, and some will have other effects entirely. Invisible units are still fully or partially affected by spells which affect an area.

Sources of Invisiblity

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True Sight
True Sight allows a unit to see Invisible enemies that are in range. Fountains, the Ancients, and all Towers passively have permanent True Sight aura. Their radius is 900 and the effect lingers for 0.5 seconds after getting out of range. Some of the listed spells provide True Sight only during certain situations. Spells which provide shared vision are not listed here, since it is not actual True Sight. A list for that can be found here.

Sources of True Sight

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Dodging abilities with invisibility
All abilities that grant invisibility will disjoint projectiles, unless the enemy has True Sight over the unit, in which case the projectile will still keep track of the target until it leaves the radius of True Sight. All physical attack projectiles of each unit and hero, as well as many spell projectiles can be disjointed. Undisjointable spell projectiles fully affect invisible units.

While most abilities affect units even if they are invisible, some will only partially affect invisible units, and many will not affect them at all. These include mostly target-seeking abilities and very few area effect abilities.

Abilities which do not affect invisible units
Additionally, the chain lightning abilities of the Harpy Stormcrafter creep and the items Maelstrom and Mjollnir do not bounce to invisible units.