“Any time you open your Vault Door, you're broadcasting an invitation for these beasties to come to your Vault and destroy your resources. Be sure to have Stimpaks and Weapons at the ready, or they'll tear through your Dwellers like a knife through a Fancy Lad Snack Cake”— In-game description, under help.
Deathclaws are the strongest enemies in the game and can be encountered when they randomly attack the vault, similar to raiders, however, they are much stronger and rarer than raiders. They can also be found while exploring the wasteland.
They can also be encountered during quests. Their boss variant with a skull on their health bar (Alpha deathclaw) is tougher, stronger, and larger in size; it can let out a roar that greatly increases its allies' next attack; this ability can be interrupted. They yield (especially the boss) the highest experience when killed.
A regular deathclaw. They can be found out in the wasteland or can attack the vault at any time once the vault reaches 60+ dwellers.
A vastly stronger and more aggressive deathclaw. Their powerup is that they can increase the damage done by other deathclaws in the room on a quest for a period of time.
A deathclaw currently under the control of the Enclave. They are trained to kill everything in their path.
According to in-game information, deathclaws are more likely to attack the vault if the vault doors are opened, immediately after sending dwellers to the wasteland or on quests, and if there is a radio station broadcasting out to the wasteland.
Deathclaws will begin to attack when the vault has 60+ dwellers. They will start attacking at 35+ dwellers when playing in Survival mode.
Deathclaws will not drop any type of weapon, armor, or caps. They will only provide XP upon death.
Deathclaws do not use the elevator to move up or down through the vaults levels, instead they appear to smash through the shaft's floor to the next level.
↑Fallout Shelter. Status updates from exploring dwellers state "Enclave deathclaws are trained to kill - this will be a fight to the death!" and "The Enclave Deathclaw is trained to kill anything in its path I have to run"