It's been proven that flies can see 360 degrees and have several other sensors at their disposal, making them very difficult to swat. For a long time, I just rolled up a magazine and swung furiously until I eventually killed the fly, leaving a splotch of tiny guts for me to clean. Then one day I tried something—something new, something innovative. I dampened a paper towel and threw it at the fly. The paper towel hit the wall with a smack and stuck there, trapping the fly against the wall and allowing for easy disposal.
I'm not sure why this technique works so well. I'm not sure why the flies can't see it coming, but they don't. Maybe it's too fast for them. Maybe it's the color of the paper towel. I'm not sure, but it get's them every time.