Gamma World doesn't have levels as such, but it might as well. Every so many thousand experience points (starting at 3000 and roughly doubling at every step after that), a player gets to make a 1d10 roll on a table to determine the bonus his character gains from experience. 60% of the time, the bonus is a +1 to specific ability score (but no score can exceed 18), 20% of the time, the bonus is +1 to hit in physical combat, and 20% of the time, the bonus is +1 per die inflicted by non-energy weapons.
Experience points are awarded first for defeating enemies at a rate of 1 XP per hit point of the defeated enemies. Even compared to OD&D Supplement I's revised XP charts, that's a very small amount. Secondly, XP is awarded for finding artifacts, at rates listed in the rulebook. The XP amounts vary according to the type of artifact, with grenades, for example, awarding only a couple of hundred XP, while a high-tech rifle might award a couple of thousand. It's worth noting that XP is also given for the worth in gold pieces of valuable non-artifact items. As you can see, finding artifacts (and other items of value) is thus the ticket to advancement in the game, much as treasure is in OD&D. Thirdly, the referee may award XP "for outstanding actions." Just what constitutes an outstanding action or what an appropriate XP award for it might be is not stated.
XP is awarded on both an individual or group basis. Combat XP is divided equally amongst all combatants, provided they all participated equally. Characters who don't do so or who sneak away in the midst of battle ought to be awarded less (or no) experience. XP from artifacts or items of value, however, are awarded to individuals. In general, such XP seems to go to the character who figured out how to operate the artifact and can therefore use it.
All in all, Gamma World's experience point award system is very reminiscent of those in old school D&D but (once again) pointing the way toward the more "story-oriented" approach that would be adopted more broadly later on. On the other hand, "level" advancement means comparatively less than in D&D, with its benefits being random and potentially non-existent depending on how one rolls. I've sometimes found myself imagining what D&D might have been like if advancement were similarly unpredictable.