... Several studies have looked at the possible effects of binaural beats within the alpha range on cognitive abilities. A significant improvement in cognitive processing, as measured by the Stroop Effect exercise, was found by a BB stimulation of 10.2 Hz frequency (Cruceanu & Rotarescu, 2013).Carter and Russell (1993)exposed 8 to 12 year old boys with learning disabilities to 8-week long 10 and 18 Hz BB stimulation sessions, and they found an improvement in Raven's progressive matrices and in a subtest of auditory sequential memory (Carter & Russell, 1993).McMurray (2006)assessed the effect of 7 and 11 Hz BB on alpha brainwave activity, working memory, and attention in healthy elderly people, who are known for experiencing gradual decrease in physiological alpha activity. The 2 minutes exposure to BB resulted in an altered electrical activity in the brain. ...
... [9] While entrainment by binaural auditory beats in the alpha frequency has also been shown to enhance creativity, cognition, memory, and an improvement in intelligence tests and achievement tests in learning disabled boys. [10][11][12][13] The gamma-band activity has been shown to involve in a variety of functions such as attention, memory, and consciousness. Current literature suggests that entrainment by gamma beats promotes cognitive flexibility, modulates visual attention, and enhances creativity. ...
The final suggestion I have to offer is that you make your practice a regular, consistent habit. You don’t have to be perfect but you do need consistency. Like any other skill, entering meditation will develop in direct proportion to the consistency of your practice. Missing a session occasionally is not going to derail all your progress. But frequently skipping or blowing insincerely through practice is not going to produce any noteworthy results. There isn’t any hard and fast rule from frequency of practice that always applies to everyone, but most of us will instinctively know whether or not we’re giving our practice the time and effort it requires.
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.
Because the brain filters and interprets reality in a split-brained way, we tend to see things as separate and opposed, rather than as connected and part of the oneness spoken of by the great spiritual teachers (and, in the last few decades, by quantum mechanical physicists). Thus, at a deep level, the dual structure of our brain, in conjunction with brain lateralization, predisposes us to see and experience ourselves as separate from, and often in opposition to, the rest of the world—instead of experiencing the elegant interconnectedness between us and everything else. Our childhood associations and programming build on this inborn tendency by training us to seek this and avoid that, to move toward pleasure and away from pain, to do good and not bad, and so on. The greater the lateralization in the brain, the greater the feelings of separation—and the greater the feelings of separation, the greater the fear, stress, anxiety, and isolation.

Theta is very subtle. It is one of the most elusive and extraordinary brain states you can explore. Theta is a state of somnolence with reduced consciousness; you are neither fully awake nor asleep yet. It is also known as the “Twilight state” or “Stage 1 Sleep” which you normally only experience fleetingly as you wake or drift off to sleep. In the Theta brain state, your senses are withdrawn from the external world and focused on signals originating from within.
Why not? Because the flushing has nothing to do with the brainwaves or entrainment, and everything to do with the expectations we bring to the use of entrainment. We didn’t watch that sunset with any expectations of face flushing. We didn’t have any of those expectations while listening to that music. In short, there is a cause generating the effect, but the cause is our expectations, (excellent Article here) not the entrainment.
“Binaural beats are not very noticeable because the modulation depth (the difference between loud and quiet) is 3 db, a two-to-one ratio. (Isochronic tones and mono beats easily have 50 db difference between loud and quiet, which is a 100,00-to-1 ratio). This means that binaural beats are unlikely to produce an significant entrainment because they don’t activate the thalamus.”
Passively listening to binaural beats may not spontaneously propel you into an altered state of consciousness. One's subjective experience in response to binaural-beat stimulation may also be influenced by a number of mediating factors. For example, the willingness and ability of the listener to relax and focus attention may contribute to binaural-beat effectiveness in inducing state changes. "Ultradian rhythms in the nervous system are characterized by periodic changes in arousal and states of consciousness (Rossi, 1986).
Entrainment is a phenomenon by which some external sensory stimulation synchronizes brainwaves differently than the native rhythm. The most obvious example of this is photic driving – during an EEG the subject will have a strobe light flashed before them at various frequencies. The purpose of this is to see if it will trigger seizure activity. In many normal subjects the brain wave rhythm in the occipital lobes, which is the visual part of the cortex, will match its frequency to the frequency of the strobe light. This specifically is called photic driving, but the phenomenon in general is called entrainment.
The Neuro Programmer website, as is typical, is full of testimonials and vague references to research. I tried to track down the research they referenced, but could not find anything published or peer-reviewed by the authors named or on the subjects indicated. For example, they cite one study by Thomas Budzynski, but the only thing published by him that is listed on Pub Med is a small study on biofeedback published in 1969. The 1999 study they reference is not listed. Also – Budzynski has connections to another company – Theta Technologies – which sells similar technology.  (The exact nature of his connection is not clear, he was at least a consultant. He is also listed as the director of research for another company, Synchromed, LLC.)  This looks like just another in-house worthless study to support the marketing of a product.

Cortisol is an arousal hormone, stimulating alertness and attention. Cortisol levels rise and fall in connection to circadian rhythms—cortisol levels rise to their peak levels first thing in the morning, just in time for you to be active for the day. Too-high cortisol levels are associated with insomnia, as well as more time spent in light sleep, rather than deep sleep.

The Frequency following response (FFR), also referred to as Frequency Following Potential (FFP), is a specific response to hearing sound and music, by which neural oscillations adjust their frequency to match the rhythm of auditory stimuli. The use of sound with intent to influence cortical brainwave frequency is called auditory driving,[39][40] by which frequency of neural oscillation is 'driven' to entrain with that of the rhythm of a sound source.[41][42]