Pre-Crisis (1980 - 1985)
When originally introduced in DC Comics Presents #27/28, Mongul was only given a cursory origin. It was explained that he had been the ruling despot of his race's homeworld, until they finally got tired of him and overthrew him in a revolution. He then escaped (or was exiled) and decided to get revenge on his people by taking over Warworld and using it to destroy his own planet. The original version towered over Superman and proved to be his physical match when they fought. In each case, however, Superman proved to be the stronger of the two.
Post-Crisis (1985 - 2011)
After the Crisis on Infinite Earths retcon, Mongul was largely unchanged with two notable exceptions - he was now closer to human-size (yet still quite large), and he was now the ruler of Warworld, a planet where the populace was kept docile through gladiator games that were broadcast across their world. Eventually, Mongul would lose his throne in this version as well, and thereafter seek revenge against the Justice League, specifically Superman.