The current version of the article has already undergone one round of review. Reviewer A considerably changed the article by rearranging the material, removing some topics and references, and adding new discussions. This changed the logical flow of the text, for example, the original sequence "from weak to strong turbulence" was changed to "from isotropic to anisotropic". A new notation was introduced: "KID's" model instead of the standard "IK" (Iroshnikov-Kraichnan). The discussion of the variations of the IK model and the renormalization group approach was added, which somewhat diverts from the original discussion of the basic ideas. The open questions formulated in the original version were removed. More essential, the statements regarding the spectrum of MHD turbulence were altered throughout the article. The new claim “numerical simulations tend to favor -5/3 energy spectrum even when the mean magnetic field is stronger compared to the fluctuations” was added, which seems to be a questionable statement, since recent high resolution numerical simulations favor -3/2.
Since the author has not yet responded to these changes, in my review below I refer to the original version of July 29, 2008.
This article is an excellent brief account of modern views on MHD turbulence, the problem that is still far from being solved. Our present understanding relies on phenomenological arguments and numerical simulations. The article discusses developments on which there seems to be a consensus among independent research groups. Among those developments are the Iroshnikov-Kraichnan view of MHD turbulence as an ensemble of counter-propagating Alfven modes, the Goldreich-Sridhar phenomenology of anisotropic turbulence, the theory of weak turbulence, the picture of dynamic alignment. It is reasonable to believe that these ideas will be integrated, in some form, in the future rigorous theory of MHD turbulence. Some very recent questions, such as imbalanced MHD cascades, are still awaiting systematic study and, probably, larger computational resources. These open questions are listed in the end of the article.
I believe the article needs only few minor changes:
1. The definition of v_\lambda and b_\lambda after formula (6) could be given. These are “typical,” that is, root mean square velocity or magnetic field differences across separation \lambda.
2. In subsection “strong balanced cascades”, when the critical balance is discussed, it may be better to use \lambda_\perp and \lambda_||, rather than k_\perp and k_|| . Indeed, for the Fourier transform one needs to specify the rectangular domain. Since the direction of the local magnetic field is itself a function of scale, such domain is not defined. It is better to speak about the field-parallel and field-perpendicular sizes of the eddies.
3. In the same subsection, one could add a reference to Muller & Grappin, Physical Review Letters, vol. 95, Issue 11, id. 114502, 2005, where the spectral exponent -3/2 was first observed in direct numerical simulations with very high resolution of 1024^2 in the field-perpendicular direction.
4. In subsection “strong imbalanced cascades” one could add a reference to Perez & Boldyrev (2009) Phys. Rev. Lett. (http://arxiv.org/abs/0807.2635), where high-resolution numerical simulations of strong imbalanced MHD turbulence were performed and compared to existing models.