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Wario's in-universe origins have never been completely explored in the games, however there have been attempts to explore his back-story in various officially licensed comics.

The comic "Super Mario: Die Verwandlung" (which translates to Super Mario: The Transformation) shows Wario merging from Mario as a result of a procedure by Dr. Light to cure Mario from his pixelation.

The comic "Mario vs. Wario" shows that during youth, Mario and Wario, when playing together, would often result in Wario getting either hurt or humiliated, believing Mario to be the cause for his bad luck.

The second comic, "Warios Weihnachtsmärchen" (which translates to Wario's Christmas Tale), a parody of A Christmas Carol, shows a flashback of Wario and Mario as babies building sandcastles but because Wario was mean to everybody, Mario would receive all the attention. Also during a graduation ball, Wario wanted to dance with Peach, Princess Toadstool, however because Mario was much nicer to her she instead danced with him.

While all these comics were officially licensed, they have never been acknowledged by Nintendo. Wario has however appeared as a baby in "Yoshi's Island DS".
Contributed by KnowledgeBase
The idea for WarioWare's fast action microgames originated from a Japanese game called Mario Artist: Polygon Studio for the Nintendo 64DD. The game featured a game mode called "Sound Bomber" which features many of the microgames that later made it into the WarioWare games.
Contributed by Koopaul
It's easy to assume that Wario's name was based on turning the M in Mario's name upside down, but this isn't entirely the case. The Japanese word for 'bad' is 'warui', so Wario is actually a shortened version of 'Warui Mario' (Bad Mario). This is also the case for Waluigi (Bad Luigi), and works even better in Japan, where his name is pronounced 'Waruigi'.
Contributed by DidYouKnowGaming