  We review, systematize and discuss models of diffusion in neuronal tissue, by
putting them into an overarching physical context of coarse-graining over an
increasing diffusion length scale. From this perspective, we view research on
quantifying brain microstructure as occurring along the three major avenues.
The first avenue focusses on the transient, or time-dependent, effects in
diffusion. These effects signify the gradual coarse-graining of tissue
structure, which occurs qualitatively differently in different brain tissue
compartments. We show that studying the transient effects has the potential to
quantify the relevant length scales for neuronal tissue, such as the packing
correlation length for neuronal fibers, the degree of neuronal beading, and
compartment sizes. The second avenue corresponds to the long-time limit, when
the observed signal can be approximated as a sum of multiple non-exchanging
anisotropic Gaussian components. Here the challenge lies in parameter
estimation and in resolving its hidden degeneracies. The third avenue employs
multiple diffusion encoding techniques, able to access information not
contained in the conventional diffusion propagator. We conclude with our
outlook on the future directions which can open exciting possibilities for
designing quantitative markers of tissue physiology and pathology, based on
methods of studying mesoscopic transport in disordered systems.
