The more spies you have on a race's planets, the faster you will learn more about them. There are several levels of Espionage: Low, Medium, High, Advanced... and I think there's at least one more after that, but I don't remember. Each level gives you more access to their stats. By the time you have a HIGH espionage level on them, you can double-click to view their planets as you would view your own, and look at what ships they're making.