Binaural beats are a form of “auditory beat stimulation”, which includes both monaural and binaural beats. They can probably alter the abundance of certain brainwaves, which may improve or alter mental states to make users better at memorization, paying attention, or relaxing.
The beats are formed by playing two tones with slightly different frequencies in unison. A monaural beat is formed when these tones are combined before they are played through a speaker, whereas a binaural beat is formed when each tone is played separately into each ear, producing a perceived third tone that is equal to the difference between the two base tones. For example, an individual may have a 240 Hz tone played in one ear and a 245 Hz tone played in the other, which will produce the illusion of a third 5 Hz tone.
Binaural beats are an auditory illusion produced by playing two slightly different tones into each ear, and are tuned to the frequency of certain brainwaves to produce a desired effect.
Adverse effects of binaural beats are rarely reported, although no safety trials have been conducted. Additionally, the frequency of binaural beats matters, and some may impair certain types  of cognition transiently. Of course, listening to beats too loudly can potentially damage hearing.
Although we did not find any research suggesting this, binaural beats could theoretically produce a negative effect in people with some sort of pre-existing neurological condition, simply due to the wide variety of possible interactions any intervention would have with diverse conditions.
There isn’t much safety data related to binaural beats, but they are likely safe. People with hearing or neurological conditions should exercise more caution.
Although the mechanism is still under investigation, it is thought that binaural beats elicit a “frequency following response” (FFR) , which is the tendency of the electrical activity in the brain to match the frequency of an external periodic stimulus such as a tone.
By playing the perceived third tone at a certain frequency, the brain should (theoretically) increase the presence of brainwaves of the same frequency. Because different brain wave frequencies are associated with different types of mental activity, the binaural beat frequency could be used to improve certain types of cognition or produce specific moods. Some studies have successfully measured an FFR from binaural beats using electroencephalography (EEG), although other studies have failed to find this effect.
Binaural beats may increase production of brainwaves of the same frequency, which may help facilitate certain aspects of cognition.
Because binaural beats require a unique sound played into each ear, headphones should be used.
A number of binaural beat generators are available, most of which offer the option to set a base frequency (often between 200 and 400 Hz) followed by a binaural frequency, the former being the average frequency between each of the tones played in each ear and the latter being the difference between the two frequencies.
Binaural frequencies are often set to match certain brainwave frequencies, depending on the desired effect: 
Delta (1–4 Hz) – Sleep
Theta (4–8 Hz) – Sleepiness, meditation
Alpha (8–13 Hz) – Moderate alertness, meditation, recall
Beta (15–20 Hz) – Focus, sustained thought, excitement
Gamma (32–100 Hz) – Learning, problem solving
Note: Certain types of brain damage can impair an individual's ability to hear binaural beats. For example, individuals who experienced aphasia after a severe cerebrovascular accident (stroke) did not show any response to binaural beats. Also, older individuals may not respond to binaural beats as effectively as younger individuals, especially at higher frequencies. 
To use binaural beats, tune them to the frequency of a desired brainwave and listen using headphones. A number of binaural beat generators can be found on the internet.
Although binaural beats have been studied in diseases such as Parkinson’s, cardiovascular disease,  and tinnitus, the bulk of the research has been dedicated to improving sleep, cognitive factors, and pain. Broadly speaking, binaural beats seem to have modest to strong effects on sleep, memory, attention, mood, and pain.
A quick note about the studies: the “control” groups vary considerably, and include silence, white noise, music, and sham sounds. Developing adequate controls is difficult with a treatment like this, which is worth keeping in mind.
There have been two studies that evaluated the efficacy of binaural beats on sleep, which have found some positive effects:
The first study, conducted in 21 people, found that using theta and delta binaural beats for 20 minutes prior to a nap had no effect on sleep latency (time to fall asleep), but did improve sleep stability (the regularity of the sleep-wake cycle) compared to silence.
The second study, conducted in 15 elite young soccer players, found that eight weeks of sleeping with binaural beats in the delta and theta range improved sleep and awakening quality, reduced daytime sleepiness, and improved mental state compared to silence.
Delta and theta binaural beats have shown some promise for improving some sleep parameters, but the jury is still out.
An uncontrolled study of 58 people  found that a 5 minute exposure to gamma binaural beats was sufficient to produce gamma waves in the brain, and that gamma waves measured during a long-term memory test were directly proportional to performance on that test, although binaural beats were not used during the test itself.
In a two-armed crossover study  of 32 people, participants received white noise preceding or following binaural beats 15 minutes prior to a memory task, and two minutes during. Half of the participants received theta beats and half received beta beats. Interestingly, the participants who listened to beta beats experienced improved free recall and word recognition, whereas those who listened to theta beats actually did worse. The researchers suggest that this may be because theta waves are associated with “states incompatible with the encoding of information” such as relaxation, decreased anxiety and activation, and increased hypnotic susceptibility.
A study of 34 people  compared the effects of silence, a pure 240 Hz tone, classical music, and binaural beats at 5, 10, and 15 Hz on a verbal working memory task, and saw that the 15 Hz (beta) beats significantly improved performance. 5 and 10 Hz beats had no effect.
Another study in 28 people  used the same experimental design, but instead tested visuospatial memory, and found 15 Hz produced a significant improvement in performance. Silence and 10 Hz beats produced the worst performance and the other interventions had an intermediate effect.
In a study of 24 participants, 40 Hz (gamma) binaural and monaural beats produced significantly better performance on reaction time in an attention test (the Flanker test), with equal overall performance compared to white noise. There was no improvement in working memory, and and working memory tests compared to white noise. There was no difference between those who received binaural and those who received monaural beats.
A uncontrolled study of 25 people  found that receiving binaural beats in the delta, theta, and alpha ranges while sitting in a massage chair had significantly reduced mental fatigue and improved attention, verbal short and long-term memory, and non-verbal long-term memory than those who received only massage.
Beta and gamma binaural beats may improve working memory. Other ranges could potentially make these aspects of memory worse (acutely).
24 participants listened to white noise, 40 Hz gamma binaural beats or monaural beats while performing an attention test and a working memory test with two minutes between tests. The binaural and monaural beat groups performed better on both tests, and there was no difference between the binaural and monaural beat groups.
A study of 20 children and adolescents with ADHD  found that 20 minutes of beta beats, thrice weekly for three weeks did not improve any measures of attention compared to a sham treatment, although parents reported fewer homework problems.
In a study of 36 college students, gamma beats did not improve the suppression of irrelevant information during an attention task, but did increase visual attention compared to control.
There is some evidence (particularly with gamma frequencies) that binaural beats could improve ADHD, but so far the results are mixed and further research is required.
One study, conducted in 24 people, has investigated the effect of binaural beats on divergent (e.g., answering “how many ways can you use a piece of paper?”) and convergent (e.g., answering “what single word could be put in front of ‘market’, ‘star’, and ‘hero’?”) creativity.
This experiment exposed participants to alpha or gamma beats with white noise or a constant 340 Hz tone for 3 minutes prior and during a creativity task. Additionally, striatal dopamine levels were estimated using “eye-blink rates” (EBRs). Both alpha and gamma beats seemed to improve divergent thinking in people with low EBRs (<20 blinks/min), but actually impaired those with higher EBRs. The researchers suggest that those with low EBRs have low dopamine and have more room for improvement, or it could be because dopamine improves neural synchronization which helps people who are lower, but creates more noise for those who are sufficiently high.
A study of 40 college students  found that listening to gamma binaural beats while sorting two separate groups of numbers improved cognitive flexibility compared to those who listened to a 340 Hz tone. In this study, “cognitive flexibility” was measured as the ease with which participants moved from working with one group of numbers to another.
Creativity is a difficult concept to test, but a small amount of evidence suggests that gamma and alpha beats may improve it in some respects. One study suggested that baseline striatal dopamine levels will influence if you respond positively or negatively to treatment, so further research is required.
A study of 104 patients  undergoing elective surgeries found that receiving binaural beats using delta frequencies significantly reduced pre-operative anxiety compared to music alone or silence.
A trial of 64 college-aged students  found increased parasympathetic tone (as measured by heart rate variability) after exposure to theta beats, although there was no difference in reported stress levels compared to control.
In a study of 60 patients undergoing dental surgery,  alpha beats given immediately after local anaesthesia significantly reduced preoperative anxiety compared to control.
A study in 32 people  found that relaxing music paired with alpha binaural beats was more relaxing than the participant’s favorite music, as measured by blood pressure and heart rate, although it did not increase the presence of alpha waves as measured by EEG. A second part of the study saw that listening to the same relaxing music plus alpha beats for 30 minutes daily for a week could increase overall alpha wave production in the brain, but did not have any long-term effects on heart rate and blood pressure.
An uncontrolled study of 14 people  found that three minutes of exposure to theta, alpha, beta, or gamma beats did not alter EEG readings or produce changes in emotional arousal as measured by skin conductance and rate.
In a study of 15 young and 15 elderly people, meditative music paired with theta beats had a more relaxing effect in classical music in young people, but classical music was more relaxing in elderly people.
An uncontrolled study of 25 people  found that those receiving binaural beats in the delta, theta, and alpha ranges while sitting in a massage chair had significantly reduced mental fatigue and improved attention, verbal short and long-term memory, and non-verbal long-term memory than those who received only massage.
In a study of 21 individuals, 20 minutes of theta beats increased parasympathetic and decreased sympathetic activation post-exercise compared to control, as measured by heart rate variability.
Delta, theta, and alpha beats have been shown to reduce anxiety and improve parasympathetic tone. This effect is most consistent in preoperative patients, and may not be as effective in older adults.
In a study of 49 boys receiving propofol and caudal blockade  (epidural) for sub-umbilical surgery, delta beats were able to reduce the amount of propofol required for anaesthesia compared to control.
A crossover study of 17 people with chronic pain  found that one 30 minute session of theta beats in lab conditions plus unlimited use for one week reduced pain intensity, psychological stress, and analgesic use compared to a sham treatment.
In a study of 40 individuals  who underwent total knee replacement surgery, those who received delta beats prior to surgery used nearly 50% less morphine in their first postoperative day compared those listening to a constant 256 Hz tone.
In 36 adults with chronic pain, 20 minutes of theta beats daily for two weeks significantly reduced pain intensity compared to a sham treatment.
Theta and delta binaural beats seem to improve pain for individuals who have chronic pain or are undergoing surgery, although the few studies conducted thus far have been short-term in nature (measuring response either immediately or after two weeks).
While binaural beats have been investigated for a variety of outcomes, the best evidence lies in their effects on memory, relaxation, and pain.
Lower-frequency binaural beats in the delta, theta, and alpha ranges seem to produce relaxation and pain reduction, and higher frequency beats in the beta and gamma range may be able to improve memory.
Lower-frequency beats may make memory worse acutely, by producing neural states that are incompatible with encoding information.