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 believe this compromise might be agreeable. Mr. Doar? Thousands have gathered here to demonstrate their dignity. I don't want to challenge Judge Johnson. I don't want to go against the President. I don't want any of this. The President could stop this with a stroke of his pen. He chooses not to. (..)2014 Selma
(..) Proudest moment of my life, I tell you. Now civil rights is a priority - of this administration as you know. - Thank you. We're gonna face the challenge, or this country is storing up a heap of trouble for itself. Now, seeing as I can't convince you to work with my administration (..)2014 Selma