The analysis of the diffusion signal is closely related to the sampling of the q-space. (a) Full sampling of the q-space is currently impractical in vivo due to the significant acquisition time it would imply. (b) Low angular resolution sampling used in DTI. (c) High angular resolution sampling (HARDI). (d) Radial only sampling used in diffusion NMR. (e) Sparse sampling which combines radial and angular measurements. * Acquisition time for a diffusion image at full resolution is approximately 1h. * Direct processing of the data is not reliable due to the limited number of samples. * Numerous reconstruction models of the literature are described in this review. * Three groups of methods based on the nature of sampling: angular, radial and combined. Recent advances in diffusion magnetic resonance image (dMRI) modeling have led to the development of several state of the art methods for reconstructing the diffusion signal. These methods allow for distinct features to be computed, which in turn reflect properties of fibrous tissue in the brain and in other organs. A practical consideration is that to choose among these approaches requires very specialized knowledge. In order to bridge the gap between theory and practice in dMRI reconstruction and analysis we present a detailed review of the dMRI modeling literature. We place an emphasis on the mathematical and algorithmic underpinnings of the subject, categorizing existing methods according to how they treat the angular and radial sampling of the diffusion signal. We describe the features that can be computed with each method and discuss its advantages and limitations. We also provide a detailed bibliography to guide the reader.