How do you view challenges?

Throughout the game messages saying "Challenge such and such complete" will pop up. So far I can't figure out exactly how to look these up or figure out what they mean. Anyone have any information?
 
EDIT: Since I messed up and put this in general discussion I should clarify I meant in Borderlands.

" Throughout the game messages saying "Challenge such and such complete" will pop up. So far I can't figure out exactly how to look these up or figure out what they mean. Anyone have any information? "