When you play two separate frequencies in each ear, say 140 Hz and 149 Hz, the difference in frequency is 9 Hz. Your brain compensates for this difference and a third tone of 9 Hz is experienced. This will result in your brain being lowered or raised and tuned into the desired frequency. This is how binaural beats are produced. Headphones are essential for this to work.  
Really great stuff here, man. Well done! Without taking anything away from the article it would have been great to have under one “roof” similar information about hypnotherapy and subliminals. I invested quite a lot in buying binaural cd’s but after reading your material I think that for short term effects isochronic tones rather than binaurals are the technology to go for now. For longer lasting and possibly permanent effects I’m not sure whether I should go for hypnosis or subliminals (or both). An article as well written and comprehensive as yours but focusing on hypnosis vs subliminals would have completed the circle for me. The stuff I’ve read so far on binaurals vs isochronics hasn’t really done it for me. Any chance you could give it a shot?
So, in summary, binaural beats certainly do not work the way the sellers claim, but there's no reason to think they're any less effective than any other music track you might listen to that effects you in a way you like. If they make you sleepy (like they all do for me), use them to go to sleep. If they relax you or get you amped, use them for that. But don't expect them to be any more effective than regular music. If someone you know claims that they are, put them to the test, and bust the myth.
The functional role of neural oscillations is still not fully understood;[6] however they have been shown to correlate with emotional responses, motor control, and a number of cognitive functions including information transfer, perception, and memory.[7][8][9] Specifically, neural oscillations, in particular theta activity, are extensively linked to memory function, and coupling between theta and gamma activity is considered to be vital for memory functions, including episodic memory.[10][11][12]