Is there scientific evidence on the benefits of binaural beats? When two coherent sounds with nearly similar frequencies are presented to each ear respectively with stereo headphones, the brain integrates the two signals and produces a sensation of a third sound called binaural beat.

I tried to google, but a lot looks like fake evidences and not having any scientific evidences. What is the evidence for binaural beat music producing different cognitive and/or neural effects as compared to non-binaural beat music?
Since I was asked in chat about binaural beats, and have been posed this question a number of times before besides, I looked into the most recent literature using Google Scholar for the single term &quot;binaural beats&quot; and restricted my search to papers published between 2010-2015. For convenience, this is the definition of a binaural beat I will use.

When two coherent sounds with nearly similar frequencies are presented to each ear respectively with stereo headphones, the brain integrates the two signals and produces a sensation of a third sound called binaural beat (BB). — Gao et al., 2014.

State of the evidence
Broadly speaking, some research on binaural beats does exist, but the evidence presented in the studies I examined is by and large negative, inconclusive or statistically underpowered with respect to the efficacy of binaural beats' ability to improve cognition, and to whether it is even processed differently from acoustic beats at all.
Much of the research that does exist seems to be published in journals whose credibility I cannot vouch for, and this answer should therefore be taken for what it is: a cursory review of the best literature I could find, not as scientific fact.

Are binaural beats processed differently?

&quot;The perceptions of binaural beats involve cortical activity that is not different than acoustic beats in distribution and in the effects of beat- and base frequency, indicating similar cortical processing.&quot;  — Pratt et al., 2010.

Do binaural beats entrain brain waves?

&quot;We observed RP increase in theta and alpha bands and decrease in beta band during delta and alpha BB stimulations. RP decreased in beta band during theta BB, while RP decreased in theta band during beta BB. However, no clear brainwave entrainment effect was identified. Connectivity changes were detected following the variation of RP during BB stimulations. Our observation supports the hypothesis that BBs could affect functional brain connectivity, suggesting that the mechanism of BB–brain interaction is worth further study.&quot; — Gao et al., 2014.

Do binaural beats induce a frequency following effect?

&quot;Analysis of changes in broad-band and narrow-band amplitudes, and frequency showed no effect of binaural beat frequency eliciting a frequency following effect in the EEG.&quot; — Vernon et al., 2011.


Concluding remarks
What evidence exists is mixed and, at best, inconclusive. Based on this, I will tentatively say that it appears the claims put forward by many commercial binaural beats companies, while theoretically plausible in some sense, are not empirically supported in the literature.
Therefore, the most prudent position for a consumer to adopt seems to be that binaural beat music is as preferable, but no more preferable than acoustic beat music. For researchers, of course, binaural beats remains theoretically interesting.
References

Gao, X., Cao, H., Ming, D., Qi, H., Wang, X., Wang, X., ... &amp; Zhou, P. (2014). Analysis of EEG activity in response to binaural beats with different frequencies. International Journal of Psychophysiology, 94(3), 399-406.
Pratt, H., Starr, A., Michalewski, H. J., Dimitrijevic, A., Bleich, N., &amp; Mittelman, N. (2010). A comparison of auditory evoked potentials to acoustic beats and to binaural beats. Hearing research, 262(1), 34-44.
Vernon, D., Peryer, G., Louch, J., &amp; Shaw, M. (2014). Tracking EEG changes in response to alpha and beta binaural beats. International Journal of Psychophysiology, 93(1), 134-139.