In Awesomenauts, players can gain Levels and unlock more game content. Player Level is increased by completing games and gaining Solar in matches. 10000 EXP is required for a Level up. Choosing a 'naut using the random button, winning games and playing splitscreen are ways to increase the Solar rewards for completing matches.
Your level is shown at the bottom left of the Main Menu, above the announcement section, alongside your League badge, Prestige Level, and Steam username.
The maximum level on Steam is 158 (as of Patch 2.12, released on September 2, 2015), while the maximum level on consoles is 45. Once you reach the max level, you gain the option to Prestige. Prestiging resets your level back, requiring you to unlock all of the upgrades again.
(WARNING: this article is grossly outdated and in need of serious updating)