The most famous major challenge was the modern rejection of geocentrism and its acceptance of heliocentrism: that is, the rejection of the view that the sun, planets, and stars all revolve around the earth in favor of the view that the earth and planets revolve around the sun. You can understand why the ancients might have been drawn to geocentrism: it does rather look as if the heavens revolve around the earth, after all, as the sun moves from east to west during the day and then pops up again the next morning in the east.
Source: wiktionary