This Pokémon had never been seen until it appeared from far in the desert 50 years ago.
– Pokemon White Pokedex
Elgyem is based on an alien, even though Deoxys is already a Pokemon based on aliens (and Clefairies are from the Moon). Its Pokemon White entry seems to relate it to the Area 51 UFO conspiracy.
It has appeared in the anime, where it can send images through telepathy to people. I expected it to have a robotic voice, since it looks kinda robotic, but it has a rather cute and sweet voice that goes “Ligu” (because it’s Japanese name is Ligray).
Stat-wise, it’s pretty slow, but has relatively high Sp Attack, which means when EV training for Sp Attack, expect to kill lots of Elgyem.