Mongul was the ruler of his own alien race before being exiled into outer space during a revolution. He eventually became the leader of Warworld, before being murdered by Neron. His son and daughter (the new Mongul and Mongal) followed in his footsteps.
for Supes, there’s been a few instances where the alien warlord has defeated the Man of Steel. One of these instances came about during the "Key That Unlocked Chaos" arc of DC Presents in 1980. During his first appearance no less, Mongul gives the unsuspecting Superman the fight of his life, before disappearing with the key to technological battle-station, Warworld. Superman doesn’t even have chance to fight back.
Later, the "For the Man Who Has Everything" storyline (1985), by comic book legend Alan Moore, sees Mongul showing Supes who’s boss yet again. This time Mongul grows a parasitic plant that takes over Superman’s mind and fools him into thinking that Krypton never exploded and he was living a normal family life on the planet. Once Superman comes to, he and Mongul engage in a fight, and it’s only when Robin comes to Supes’ rescue that he emerges victorious.