I'll be honest, not very impressed by Civ 5's spy system.
While playing the AI would just send their spies to my capital and steal my tech, so I got into the habit of never letting the AI get close enough to even see my captial so they couldn't send spies. This also included never allowing an embassy to be placed, since it reveals your capital.
When I used spies they were so I could gain vision on a city and use said vision to bomb it and nearby units with artillery and aircraft without endangering any units of my own.
So I guess the lesson here is, they can steal stuff and provide intel on military movements if they're in the area.
While playing the AI would just send their spies to my capital and steal my tech, so I got into the habit of never letting the AI get close enough to even see my captial so they couldn't send spies. This also included never allowing an embassy to be placed, since it reveals your capital.
When I used spies they were so I could gain vision on a city and use said vision to bomb it and nearby units with artillery and aircraft without endangering any units of my own.
So I guess the lesson here is, they can steal stuff and provide intel on military movements if they're in the area.