Salmoneus was the arrogant ruler of Salmone, who forced his subjects to worship him instead of Zeus. He insisted that he was as mighty as the great God. He tied sound making contraptions like copper kettles to his chariot and insisted that the noise the contraptions made when he drove by, was louder than the sound of Zeus’ thunder. He also threw torches of light around and proclaimed that these were more powerful than Zeus’ lightning. Zeus watched him for a while, and then just struck him and his kingdom down, with a real thunderbolt. End of Salmoneus.
Sisyphus, his brother and the founder king of Corinth, was trickier than Salmoneus and gave the Gods quite a run around, before he succumbed to their superior strength.
To begin with, he violated the concept of Xenia, which assured hospitality and generous conduct on the part of a king, to visitors and traders that came to his land. Zeus was the God in charge of Xenia and Sisyphus killed and tortured his guests with impunity, much to the chagrin of Zeus.
Another time, he incurred the wrath of Zeus, by giving away the hiding place of Aegina (a love interest of Zeus) to her father, the river God Asopus, in return for having a spring flow through a certain part of his kingdom.
Zeus ordered either Hades (king of the underworld), or according to some stories Thanatos (Death), to take away Sisyphus to Tartarus, deep under the belly of the earth and shackle him there for eternity. However Sisyphus tricked the God into showing him how the shackling system worked, and in the process Sisyphus shackled the hapless God and returned to the surface of the earth.
Later when he actually died and was sent to the world of the dead, he convinced Persephone, the Goddess of the Underworld, that it was all a terrible mistake and got himself sent back to the world of the living.
Ultimately, Zeus pinned him down and punished him with an endless useless back breaking job. Sisyphus was condemned to keep rolling a heavy boulder up a mountain, which then would always fall back to the ground from the top, and Sisyphus would have to repeat the thankless job for eternity. The term Sisyphean task has since come to mean a useless and repetitive task.
Thus ends the story of the two sons of King Aeolus. One thought he was as grand as Zeus and the other thought that he was smarter than Zeus and other Gods.