How do duels work, and what's the point?

I've always wondered but haven't asked until now, but, what's the actual point of duels? do they give some kind of benefit to a player's profile? do you get a notification if you are challenged? Are you notified if you win or lose that duel? All of the questions!
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I also use it for practicing with newer champs, for example I recently took 5* Wasp to r3 and wanted to try her against different champs. I found her to work quite well against Mordo.
Where can I find this?