This talk examines current diffusion MRI modeling approaches for brain tissue. Biophysical models and signal representations are contrasted. How diffusion coarse-graining facilitates modeling is explained. Emphasis is put on the identification of common modeling assumptions and examples on how to validate them. High diffusion weighting and long and short diffusion times are discussed together with state-of-the-art biophysical modeling techniques on each. Finally, future directions for modeling brain tissue are discussed.