When you listen to binaural beats/tones, you are actually listening to two slightly different pitched frequencies. Each frequency goes to each of your ears independently. When this happens your brain responds by creating a third tone, making up the difference between the two frequencies. This shift in frequency then shifts your brain’s consciousness and changes your state.

Gamma brainwaves occur during creative thinking and processing of memory and language and in many learning activities. These brainwaves are not present at all when a person is under anesthesia, but return as soon as the person becomes conscious again. Multiple scientific studies have shown gamma brainwave entrainment to be helpful for reducing distractibility, improving short-term memory, improving motor coordination, and relieving migraine headaches.

Some research suggests that the benefits from brainwave entrainment can last a lot longer, and still be seen for some time after you've stopped using it.  Study participants have still maintained improved test scores a few weeks after the stimulation had ceased.  Research on the long-term benefits has so far been minimal though, so how long the effects last is still up for debate.

Only 4 of the participants reported no change as a result of the stimulation. Four years later in a study (1989) by Anderson analyzed LED photic stimulation for the treatment of headaches. There were 60 patients included in the study which involved Variable Frequency Photo-stimulation (VFP) with specialized goggles that contained light-emitting diodes.
Isochronic tones work just the same in delta as they do in alpha, theta and beta and they are widely used in the brainwave entrainment community to help people sleep. Like you, I’ve also seen some websites saying they don’t work in delta, but it’s a bit like the game of Chinese Whispers, where someone makes a comment and then after it gets passed around and shared a lot the message gets distorted and appears to be a fact. I don’t know of any scientific reason why they wouldn’t work in delta. I remember some people talking about this on a brainwave entrainment forum many years ago. They were saying they found isochronic tones a bit too abrupt for using to help them sleep and they preferred binaural beats, as they thought they were a more soothing sound. That was just a personal preference shared by a couple of prominent forum members at the time and some people then took that as a fact for everyone. That’s where I think that belief originated from.
There are differences between high (over 18 hertz), mid (15 to 18 hertz), and low range beta states (12 to 15 hertz). Low beta states are more relaxed while still being focused, making this a good range for many daily work related tasks like balancing a checkbook, making a shopping list, or driving to a new place. However, people with attention deficit disorder lack the mental focus for doing these types of activities, and studies have found people with ADD are often low in this range of beta brainwaves.
ADHD: In 1997, various researchers conducted a study testing whether children with ADHD (attention-deficit hyperactivity disorder) would benefit from audio-visual entrainment in a school setting. The researchers entrained a small sample of 34 students from 2 different schools. They were given audio-visual entrainment for a period of 1 month and 3 weeks at various times throughout the school day.
Basically, the brain produces a phenomenon that results in low-frequency pulsations in the amplitude (volume) and sound localization of a perceived sound when two tones at slightly different frequencies are presented separately, one to each of a person’s ears, using stereo headphones.  A beating tone will be perceived, as if the two tones mixed naturally, out of the brain. The frequencies of the tones must be below 1,000 hertz for the beating to be noticeable. The difference between the two frequencies must be small (less than or equal to 30 Hz) for the effect to occur; otherwise, the two tones will be heard separately, and no beat will be perceived.
Insomnia: Perhaps one of the most promising uses of brainwave entrainment technology is for those struggling with insomnia. While the technology is unlikely to provide a “cure” it may help those who have a high level of arousal or are “keyed-up” – reduce their level of internal arousal and sleep. Specifically insomnia that is induced by excess stress (e.g. beta activity) would likely benefit from slower wave stimulation (e.g. alpha activity) to aid the brain in transitioning into sleep.
As somewhat of a modern mystic, I have studied altered states of consciousness, but due to my monkey mind, I have only been able to experience them to a very minor degree. I have tried so many methods of meditation to little avail. But I became aware that I would not be able to progress in my spiritual life if I could not achieve at least a modicum of success in meditation.
Anxiety: In a review of brainwave entrainment research, there were several studies that investigated short-term stress relief as well as long-term stress or “burnout.” Several used modalities of auditory stimulation, while a couple used audio-visual entrainment. Those with heightened short-term stress and anxiety were undergoing medical treatments, experiencing addiction, and/or were just anxious adults.
Audio-visual entrainment (AVE) is an effective tool for dissociating the depressed/anxious person out of his/her destructive thoughts. Even with increasing anxiety, AVE has been shown to reduce heart rate … reduce jaw tension from stress … increase blood flow in the eyes … and increase peak-alpha frequency … Many homes have two to three [AVE] systems in them for family members to use following a stressful, tiring day in the modern world.
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Mood: While brainwave entrainment may not be a great option for depression, particularly in the slower frequency ranges, beta entrainment may improve certain measures of mood. Additionally it is important to consider the fact that many people experience detrimental changes in mood as a result of heightened stress and anxiety. Since brainwave entrainment has been shown to improve stress and relaxation, overstressed individuals may experience a simultaneous mood improvement.
Until NeuralSync™, brainwave entrainment involved inferior linear, single or sequential protocols - such as binaural beats or isochronic tones - that were natively restricted in their ability to affect the natural complex dynamics of the brain. But now, NeuralSync™ significantly improves entrainment by incorporating EIGHT SEPARATE BUT SYNERGISTICALLY-INTERACTIVE DIMENSIONS into a dynamic and cohesive process powerful enough to compel the brain to produce whole-brain synchronization for intense effect. Incredibly superior to binaural beats or isochronic tones, NeuralSync offers an entrainment experience beyond anything you've used before.
Both brainwave entrainment and neurofeedback deal with brainwaves, but the similarity stops there. Entrainment pushes your whole brain into a pre-determined state, while neurofeedback teaches you how to move specific parts of your brain on your own. It is the differeence between forcing the brain into a given position, and skills building so you can move it there yourself.