Teleportation

Teleportation is a Unique Monster bonus. This bonus grants the monster the ability to teleport, allowing them to cover a large distance quickly, be it for running from the hero or catching up to them.

Diablo II
In Diablo II, a monster with this bonus will randomly teleport when it has less than 33% health and regain some health. If it is a ranged monster and someone is in melee range, it also teleports. Unique Bosses with Teleportation are far more difficult to defeat with Stone Skin ability, enabling them to recover health extremely fast and commonly negating all damage taken. Hitting a teleporting enemy with a cold-based spell or slowing status will reduce the amount of times an enemy will teleport, and sometimes prevent them from teleporting at all.

A good example of a monster who has this ability is Über Izual.

Diablo III
Teleportation returns in Diablo III, but it is renamed to Teleporter, and is now available to Champion and Unique monsters. In addition, certain Super Uniques/Act Bosses can also possess this or something similar. A good example of this is Diablo himself: during the fight, he will always teleport to the nephalem if he has hit them with his Bone Cage skill.

In addition, the criteria of having below 33% of total health in order to teleport is gone, which gives these monsters the freedom of teleporting as they see fit.