To struggle, fight, or compete in order to attain something. The two candidates are so close in the polls that both are vying for any kind of advantage they can find. It's nearly impossible to sit down for a meal with a friend without having the kids vie for your attention the whole time. The region has fallen into disarray as multiple factions vie for power.

To fight, contend, or compete with one (for something). Tom and I have vied with one another for top of the class since our freshman year. The embattled kingdom has been vying with three other nations for control over the region. It seems there's a new superstar in the racing world whom you'll have to vie with soon.