Page 1:
For abstract it is best to avoid terminology that is not generally known, as is the case for this phrase.  This may be defined in main text but rewording here in a more explanatory fashion is needed
% EN addressed

Page 3:
It is helpful to readers also to include references to other relatively recent reviews on magnetic fields in the ISM, including Hennebelle & Inutsuka (2019), and Crutcher (2012)
% EN addressed

It would be good to define magnetic helicity in the margin here. It does not seem to have been defined until p. 15, in the middle of a paragraph, but it would be helpful for readers to define it much earlier.
# EN addressed

Page 4:
Remove "we can" in Faraday Rotation box
# EN addressed

Figure 1:
In the caption is would be useful to indicate which is the projected major axis.
# EN addressed

Page 5:
It would be helpful to explain the winding in term of *differential* rotation, since it is not rotation itself but shear that is relevant for winding
# EN addressed

After Eq. 3:
here, lower case "u" is introduced for the velocity vector, whereas in eq. 4  uppercase "U" is used; it would be good to make these consistent.  

The adopted notation here should also be consistent with the notation that is used for mean and fluctuating parts of the flow.  Since later, b = B - \bar B for fluctuating field b and mean field \bar B, to be consistent one would have u = U - \bar U, meaning that U is the total velocity and u is fluctuating velocity.  However, here u seems to be the total rather than the fluctuating velocity.

Relating to Eq. 3:
here, lower case "u" is introduced for the velocity vector, whereas in eq. 4  uppercase "U" is used; it would be good to make these consistent.  

The adopted notation here should also be consistent with the notation that is used for mean and fluctuating parts of the flow.  Since later, b = B - \bar B for fluctuating field b and mean field \bar B, to be consistent one would have u = U - \bar U, meaning that U is the total velocity and u is fluctuating velocity.  However, here u seems to be the total rather than the fluctuating velocity.

This choice for Omega may seem puzzling to readers since constant circular velocity at large radius (with Omega = V_c/\pomega) is a better approximation for realistic galaxies than velocity varying as 1/cylindrical radius (with Omega  ~ \pomega^2).  

Page 6, Eq.4:
see previous note about notation for u, U and \bar U

Page 6, relating to "magntic diffusivity":
since this paragraph refers to microphysical conduction and electron collisions, it would be better to use the term "resistivity" here

Box "characteristic nondimensional numbers":
The viscosity nu has not yet been introduced; please define nu within the text box.

Also, for the convenience of readers  it would be good to state within the text box that (1) eta is the resistivity, and (2) k_f is a characteristic flow wavenumber

Relating to "because with zero dissipation, there can be no turbulence like that observed in real astrophysical systems":
this is a strange statement.  perhaps it would be better to say "because real astrophysical systems always have nonzero dissipation."
# EN addressed (although have some doubts on the rephrase)

Page 8 ("The tangling of a pre-existing magnetic field for eta-->0.."):
Since this paragraph is all about the eta=0 case, rather than the eta -> 0 limit, should this be revised?

Section 2.4:
Considering the central role of the alpha effect and the necessity for ARAA articles to be accessible to general readers, the article needs a brief section explaining what the  alpha effect is, both mathematically and physically.  The best place may be here, in between the current sections 2.3 and 2.4.

Presently, the Roberts flows are introduced in the text box, and then eq. 9 states without explanation that the mean EMF contains a term linear in B.   Novice/general readers will find themselves puzzled by this.

Page 9 ("in terms of an alpha effect"):
has not yet been explained

Page 10 ("For the Roberts flows, there is no mean flow, i.e. \overline{\bf{u}}=0"):
Elsewhere U is used for the total velocity, in which case \bar U rather than \bar u would be the notation for the mean flow.  To avoid confusion for the readers, it's important to keep consistent notation.

Eq. 9:
Some words of explanation regarding *why* the mean EMF has this form for Flow I would be helpful

Table 2:
what does this check mark indicate?

Page 12, Footnote 1:
Please add references as appropriate

Section 2.7 "the growth rate \lambda":
Is there a typo here?  should the gamma be a lambda?

Section 3.1:
B_eq has not been defined; please add explanation for what this represents

Section 3.1 $\alpha\propto(1+\Rm\meanBB^2/\Beq^2)$:
is \Rm a typo?

Section 3.1 ($0=\bra{(\uu\times\BB_0)\cdot\bb}-
2\eta\mu_0\bra{\jj\cdot\bb}$.)
is this 2 a typo? 

Section 3.1 ($\alpha=-\eta\mu_0\bra{\jj\cdot\bb}/\BB_0^2$):
it is not clear how this relates to the numerical result on alpha from Cattaneo & Hughs mentioned above.  More explanation is needed.

Is there a typo in the first expression citing the Cattaneo & Hughes result?  In this expression alpha is proportional to eta, whereas in the expression for alpha above cited from Cattaneo & Hughes, alpha would be inversely proportional to eta

Box "Derivation of Equation 10":
-I suggest writing as "the magnetic helicity A \dot B" to remind novice readers what this quantity is

-Since it is not done elsewhere, in this box the definition of E in terms of the other variables needs to be written (including a few words explaining this physically)

-Eq 15 --> Eq 12

Section 3.3 (It has long been anticipated...helicity fluxes)
The wording here needs to be made more clear, as this is a very important point.  EG, could say, "It has long been hypothesized that the action of magnetic helicity fluxes can overcome what would otherwise be an extremely slow approach to saturation (as described in Sections 3.1 and 3.2).

Section 3.3
it would be good to remind the reader (right after eq. 14) that \bar \cal E \equiv \bar{u \cross b} 

Section 3.3
\meanFFFFm needs to be defined

Section 3.3 (being replaced by
$-\bra{2\meanEMF\cdot\BB}$)
it would be helpful to explain why the sign is the opposite, i.e. that the sum has to be given by eq. 12

Eq. 16
-\aaaa\cdot\bb looks like an overbar is missing
-\meanFFFFf needs to be defined

Section 4.
It would help readers to provide more of a physical understanding of the role of mangetic helicity flux.  Mathematically, it has been demonstrated that if the fluxes integrate to zero, saturation is very slow.  But it would be helpful to provide some intuition about why removal of magnetic helicity might hasten the approach to saturation.

Eq. 17
I have recommended adding a short section on the alpha effect between the current sections 2.3 and 2.4.  Presumably there the simpler form of eq. 17 (multiplication only) will be given, explaining where this comes from.  Then, when the representation in eq. 17 is introduced here, it can be motivated as a generalization. 

Box "Evolution equation for nonlocality in space and time":
-Please add an explanation that eq. 18 is a model equation that assumes a certain form of alpha_ij and eta_ij, as motivated by the numerical simulations mentioned in section 4.5 (for the spatial nonlocality) 
-Eq. 20: \alpha_{ij}\meanB_j+\eta_{ij}\mu_0\meanJ_j is the plus sign correct?

Section 4.5:
highlighted "Dynamos from the memory effect"
was the intention to refer to the box "Evolution equation for nonlocality in space and time"?

Section 5.1.4:
"The first galaxies should form..."
Was this intended to be "massive galaxies"?  The first stars presumably formed within galaxies, but very small ones.

Figure 8:
a higher quality version of this figure is needed if it is going to appear in the article
# EN addressed (hr figure, hope it's enough)

Page 25:
"A very interesting approach was employed by..."
should refer to Fig 3 here with the discussion of Martin-Alvarez et al
# EN addressed

Figure 9:
A higher qualtity version of this figure is needed


Section 6.2
"the Andromeda nebula": better to use "galaxy" as this is the standard terminology
# EN addressed

Section 6.3
"dynamical quenching formalism with advective magnetic helixity fluxes included":
It would be helpful to explain this in more detail.  What is the advective helicity flux?

Section 7.4:
In numerical MHD simulations that employ finite volume methods, it is frequently the case that no explicit resistivity or viscosity is included.  However, there is inevitably effective numerical resistivity and viscosity, and only moderate Re and Re_M are achievable.   In discussing the simulations, it would be valuable to comment on this, in light of (1) the argument (section 3.1 and 3.2) that the rate at which saturation is reached is reduced at higher  Re_M, corresponding to higher resolution,  and (2) the hypothesis (section 3.3) that magnetic helicity flux -- which is present in both the shearing-box and global  simulations -- enhances mean field growth.  In particular, are there resolution studies from the simulations discussed in Section 7.3 and 7.4 that either show slower saturation at higher resolution (indicating a dominance of #1 at the achievable resolution) or convergence in saturation at higher resolution (possibly in combination with measurements of large magnetic helicity flux), supporting #2?

Figure 16:
need higher quality figure