A lot of people believe sleep has been proven to repair or rehabilitate the brain and body, but this is not necessarily true. We don't really know how much sleep. There's no clearly defined biological reason for it, and it is intuitevely an evolutionary disadvantage.
In the late 1930's a wealthy amateur scientist named Alfred Lee Loomis and his colleagues watched an EEG monitor for brain electrical activity during sleep, and they made a pretty remarkable discovery: there are actually five main parts to each of several phases of sleep that occur during a normal night. One of these stages is called REM (rapid eye movement), and it is where most of the benefit of sleep comes from. Ironically, It is in REM sleep that the brain looks the least asleep. In fact, it looks awake. This is the phase where dreams occur.
It seems that all you really need to survive and feel rested is the REM phase, which is only a tiny portion of your actual sleep phases at night. You only spend 1-2 hours in REM sleep during any given night, and the rest is wasted on other seemingly useless phases. This is where the opportunity to hack the brain presents itself. What if you could find a way to cut out the other phases and gain 4-5 more hours of productive wakeful time.
One of the ways to force your brain into REM sleep and skip the other phases is to make it feel exhausted. If you've gone to 24 hours without sleep, you might notice that you drift away into dreams straight from being awake. This is because your body goes instantly into REM sleep as a protection mechanism. The way to hack yourself into entering REM sleep without being exhausted is to trick your body into thinking you're going to get a tiny amount of sleep. You can train it to enter REM for short periods of time throughout the day in 20-minute naps rather than in one lump at night. This is how polyphasic sleep works.
With monophasic sleep, you sleep for eight hours and you get about 2 hours of good REM sleep. This is the normal schedule most people use, and it means about 5 hours of the night are lost to (as far as we know) unnecessary unconciousness.
There are five methods for polyphasic sleep that all focus on many 20-minute naps throughout the day and possbily a couple hours of core sleep at night. The most simple is the "Siesta" method, which includes just one nap in the day and then a huge chunk of sleep at night. Remarkably, adding just one nap during the day shaves an hour and forty minutes off your total sleep requirement.
The "everyman" method is just a stepped ladder acting as a guide to show how much core sleep to have for any number of naps. The amount of total sleep per day is drastically reduced for each extra nap you add.
The "uberman" method has six naps and no core sleep. Amazingly, you can function with just 2 hours of sleep using the uberman method.
How awesome would it be to sleep a total of two hours a day and feel rested? Very awesome, of course, but there is a catch. The more naps you have (and thus the less sleep you have total) the more rigorous you have to be regarding your nap times. You can't miss a nap by more than couple hours in the 2 and 3 "Everyman" methods, and you must have your naps within 30 minutes of their scheduled times for the Uberman method. If you miss a nap, the whole schedule is thrown off and you'll feel tired for days.
The rigor of keeping the schedule makes most of these methods unrealistic for most people. but if you have a flexible schedule and can manage to pick a method and stick with it several months, you'll find that you feel amazing and you have a seemingly unlimited amount of time during the day to get things done.