Because of the way they are created, there may be a positive benefit from listening to binaural beats without considering the brainwave entrainment aspect, but I haven’t seen any research on that. I first discovered brainwave entrainment through binaural beats about 10 years ago now, but they didn’t do anything for me. So I’ve never been a regular user of them. I believe isochronic tones are a more effective way to produce hemispheric synchronisation because they produce a much stronger response in the brain
Joseph Kao, creator of Profound Releasing, Profound Renewal, and Sound Asleep, is a hypnotherapist and a solution-focused therapist with a private practice in Cambridge, UK. Joe was the co-developer of an acclaimed course on conversational hypnosis, and he regularly teaches hypnotherapy and psychotherapy to other therapists. He has also been the head scriptwriter for over 800 professional hypnotherapy recordings. Joe was drawn to the world of philosophy, meditation, and brainwave entrainment technology from an early age, and he’s had a daily meditation practice since 1998.
Brainwave Power Music dedicates ourselves to creating original sound therapy music, using unique Musical Compositions, Binaural Beats and Isochronic Tones as our primary sound elements mixed with different instruments and soundscapes to create a relaxed audio environment. We have one main goal: To help others through our music, be it for physical, emotional, mental or spiritual purposes. We constantly upload new music, and continue to work hard to provide new quality music for everyone.

These are very similar to binaural beats, except that instead of the audio being fed through two different channels containing two different tones, monaural beats put both tones together on a single channel. The difference is that instead of your brain producing the effect of cancelling out the wave and producing the low frequency beat, it instead mixes in the air where it is perceived by the ears, with no brain processing involved.

♥  I'm an ADHD high school student and I've found that this sound really helps me to get my homework done. Normally, I would be up very late writing essays and studying for tests because I can't sit down and focus on them, but this helps me to focus and also keeps me awake even late at night so I can continue to work. I love this site and I know I'll use it for a long time!

Brainwave Entrainment has been used possibly as far back as 200AD, where Ptolemy of the Ancient Greeks noted the effect of flicking sunlight created by a spinning wheel. The first recorded clinical application was by a French psychologist, who again used a spinning wheel but this time illuminated with a lantern instead of the sun. He noted that his patients appeared calmer when they looked into the flickering light, so he used it as a relaxation technique whenever it was needed.
Brain wave entrainment is a real phenomenon and is useful as one method of investigating how the brain works. But there is no evidence, nor any theoretical basis, for any long lasting effect on brain function or that there is any benefit of any kind. Despite this, there is a huge industry of devices that claim to train your brain waves and have a beneficial effect. I wouldn’t waste a dime on any such device.

Binaural beats are auditory brainstem responses which originate in the superior olivary nucleus of each hemisphere. They result from the interaction of two different auditory impulses, originating in opposite ears, below 1000 Hz and which differ in frequency between one and 30 Hz (Oster, 1973).For example, if a pure tone of 400 Hz is presented to the right ear and a pure tone of 410 Hz is presented simultaneously to the left ear, an amplitude modulated standing wave of 10 Hz, the difference between the two tones, is experienced as the two wave forms mesh in and out of phase within the superior olivary nuclei. This binaural beat is not heard in the ordinary sense of the word (the human range of hearing is from 20-20,000 Hz). It is perceived as an auditory beat and theoretically can be used to entrain specific neural rhythms through the frequency-following response (FFR)--the tendency for cortical potentials to entrain to or resonate at the frequency of an external stimulus. Thus, it is theoretically possible to utilize a specific binaural-beat frequency as a consciousness management technique to entrain a specific cortical rhythm.  
Binaural beats by themselves are dull for some people to listen to. But with nature sounds or ambient music, as well as either white noise, pink noise, brown noise, mixed in with the binaural beats it is more pleasant to listen to longterm. Normally it will take about 6 minutes for the brain to start becoming entrained by the binaural beats. But it is best to listen to binaural beat recordings daily that are any where between 10 minutes to an hour long.
In shamanic traditions, drums have long been used to transport the shaman out of his or her body into other realms of reality through the use of constant rhythmic vibrations. Researcher Melinda Maxfield, studying the Shamanic State of Consciousness, found that the steady rhythmic beat of the drum struck 4.5 times per second was the key to transporting a shaman into the deepest part of his shamanic state of consciousness. With the invention of the EEG (electroencephalograph) Biofeedback researchers discovered that theta brain waves oscillate at 4.5 beats, or cycles, per second. In direct correlation, we see similar effects brought on by the constant and rhythmic drone of Tibetan Buddhist chants that transport the monks and even other listeners into realms of blissful meditation.
So using the example track above, the right ear is sent a 20Hz beat, compared to a 10Hz beat in the left ear.  As the right ear receives the higher frequency of beat, this works to increase the speed of the ‘left' brain hemisphere, which can be helpful for people with conditions like ADD, who are often found to have an abundance of slow wave activity in the left brain.
But the question is: Does it have a special effect on the brain? A lot of people think so. The basic claim being made for binaural beats is "resonant entrainment". Entrainment, in physics, is when two systems which oscillate at different frequencies independently are brought together, they synchronize with one another, at whatever the combined system's resonant frequency is. Examples of entrainment occur in animals in nature; for example the chirping of crickets or the croaking of frogs. Synchronization of menstrual cycles in women is another example. Even people coming together and dancing with one another is a type of entrainment. The basic claim for binaural beats is that the perceived low-frequency beat will entrain your brain wave pattern, thus forcing your brain into some desired state.