In this paper, fundamentals and recent progress for obtaining biological features quantitatively by using diffusion MRI are reviewed. First, a brief description of diffusion MRI history, application, and development was presented. Then, well-known parametric models including diffusion tensor imaging (DTI), diffusional kurtosis imaging (DKI), and neurite orientation dispersion diffusion imaging (NODDI) are introduced with several classifications in various viewpoints with other modeling schemes. In addition, this review covers mathematical generalization and examples of methodologies for the model parameter inference from conventional fitting to recent machine learning approaches, which is called Q-space learning (QSL). Finally, future perspectives on diffusion MRI parameter inference are discussed with the aspects of imaging modeling and simulation.