If you research it, it's a hotly debated topic i.e.- it either hasn't been definitively proven/debunked or more likely, it varies person to person.
Personally, I find that doing a strenuous workout (intervals, hardcore lifting) in a fasted state generally leads to me feeling fatigued much earlier and therefore I don't get as much out of the workout as I would otherwise. This is especially true if I'm cutting carbs. Therefore, I try not to exercise unless I've eaten something within an hour prior, even if it's just a piece of fruit. If I'm walking or other low intensity activity, I find no difference. I ALWAYS eat/drink a mix of protein and carbs afterward and if you are cutting carbs, after exercise is the best time to consume them.