Zebes is the home planet of Mother Brain and her space pirates. The pirates carved a series of caverns and tunnels into the planet and built a technological infrastructure to support it all. When they acquired the Metroids they set up a facility to breed them in order to conquer the universe with the little creatures. Samus Aran destroyed the planet in the original Metroid for the NES (and the retelling of the story in Metroid: Zero Mission), however in the years that followed half of the surviving space pirates rebuilt the planet and revived the Mother Brain while the other half traveled to Tallon IV (as chronicled in Metroid Prime and foreshadowed in Metroid: Zero Mission).

Samus returned to Zebes in Super Metroid for the Super NES when she followed the dragon Ridley to the planet following his raid on the space lab Ceres where he kidnapped the last surviving Metroid. Samus had to work her way through a newly expanded Zebes complex, including the ruins of the areas she had destroyed in the first game. She managed to defeat Mother Brain and her cronies once again, and in a last-ditch maneuver the planet's self destruct system activated following the Mother Brain's death. Samus just barely escaped along with two forms of life found on Zebes: a Dachola and three Etecoons. The planet exploded in a violent energy burst seconds later, assumedly once and for all.

Zebes has a cameo in Super Smash Bros. and Super Smash Bros. Melee as the setting of several battle royales. These settings include platforms above a lava pit and Kraid's layer.

The Zebes complex itself is divided into the following zones, each connected with a series of elevators. Note that not all of the zones are available in all instances of Zebes:

It should be noted that in the opening scenes of Metroid the name of the planet is misspelled "Zebeth". This is regarded a translation error. The original Japanese name for the planet is "Zebesu" and because it's a nonsense word, the translators didn't really know how to translate it to English. They chose, for whatever reason, to call the planet "Zebeth" during the translation process. Unfortunately, whoever wrote the manual for the American release of the game picked "Zebes," and that's the one that caught on, and so the opening of Metroid comes across as a typo.


References:
http://www.classicgaming.com/mdb/genfaq.htm
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