How can people handle fire and not be burned?

Someone recently asked me about how people can handle fire. My first thought was about a chemistry demonstration called "the burning dollar," where a dollar is soaked in a 50:50 mix of water and rubbing alcohol. When a match is set to the dollar, the alcohol ignites and dollar appears to be on fire. But the water in the dollar prevents it from burning, at least for a little while (avoid ever trying this out with a $20 - and uh, no, this recommendation doesn't come from experience). They referred to a YouTube video where someone used a small piece of rag rolled up and held together with a rubber band to form a small ball. It was then soaked in some kind of fuel, and by continually moving the ball between hands, handling the burning ball was possible.

Using this technique, it is relatively easy to handle fire; and by easy, I mean that I only got a few first degree burns in the process of trying to do it. Additionally, when there is too much fuel, it drips out of the ball and onto other surfaces, subsequently lighting them on fire. Also note that in the following video, the ball is soaked with a little too much fuel, and it leaked onto my fingers (OUCH!). As a result, I give this one the "Don't try this at home" status, or, "Just watch the video instead," advice. I also found a few videos of people (whose sanity should be checked) trying to breathe fire, with disastrous results I should add. Is there a slogan somewhere that says something about only you can prevent a forest fire on your face?