OrnithoptersThis is a bit crazy, but the physics have been worked out for personal human flight using an upper body exoskelton.
It's been something dreamt of since Da Vinci, Lillienthal and many other flight pioneers... but since we've figured out how to fly using fixed wings with a rotor the idea of using wing propulsion has taken a back seat. However there's a reason nature uses wing propulsion: it's incredibly efficient. It's also much more maneuverable (but requires much more precise control). It's also an order of magnitude cooler. Imagine flying like an angel. The danger is flying too close to the sun... since something like this would be extremely dangerous.
It would initially find the most utility in the military, but as the kinks get worked out it could become something enthusiasts could use. Like surfing but in the sky.
Our current day materials, energy sources, motors, control mechanisms, and interfaces would allow for something like this to be possible for the first time. I'm honestly surprised more peole are not working on this, maybe they are behind closed doors.
So, how does it work? Probably best to just link over to Douglas C. George's website.