Unaffected by item negating effects (such as Embargo and Klutz). Item manipulating effects (such as Trick and Fling) cannot remove a Z-Crystal from a Pokémon.
An Eevium Z first appeared in SM065, where it was revealed that Kagetora had given it to Ilima after being defeated by him. Later in the episode, Ilima used the Z-Crystal with his Eevee to perform Extreme Evoboost while fighting a group of Team Skull Grunts. Eevee was given a massive power boost that allowed it to easily defeat the Grunts and send them blasting off.