Many phantoms have been developed with the aim of validating advanced diffusion magnetic resonance methods; such as microscopic anisotropy, restricted diffusion, intercompartmental exchange, pseudo-diffusion/flow, and multi-parametric correlations. Biological phantoms – such as ex vivo tissue, cell cultures, and yeast; physical phantoms – such as porous media, polymer fibers, and microspheres; and chemical phantoms – such as liquid crystals, polymers, and contrast agents; have been used to provide evidence of the ability of the proposed advanced diffusion magnetic resonance methods to extract information about a systems’ structural and functional characteristics, as well as test their reproducibility and reliability.