The new data 'challenges' many old assumptions. [=the new data gives people reasons to doubt many old assumptions]
He hopes to be the governor's 'challenger' in the next election. [=the candidate running against the governor]
The coach is confident that you will 'rise to the challenge'. [=the coach is confident that you will succeed]
(..) I couldn't let you rise to your father's last taunt. - What taunt? - The will, Robert. That will? That's his last insult. A challenge for you to build something for yourself... ...by telling you you're not worthy of his accomplishments. - What, but that he was, um, disappointed? - I'm sorry. (..)2010 Inception