The History and Status of the P versus NP question (1992) [pdf]

Just so you know the latest alleged solution seems to be wrong too: https://cstheory.stackexchange.com/a/38832/19646

For people like me who are not sure what P/NP is about, I recently listened to a podcast episode on this topic https://itunes.apple.com/us/podcast/software-engineering-rad...

Here's a much more recent and more detailed write up by Scott Aaronson:

http://www.scottaaronson.com/papers/pnp.pdf