Recently, non-Gaussian diffusion-weighted imaging (DWI) techniques, including q-space imaging (QSI) and diffusional kurtosis imaging (DKI), have emerged as advanced methods to evaluate tissue microstructure in vivo using water diffusion. QSI and DKI have shown promising results in clinical applications, such as in the evaluation of brain tumors (e.g., grading gliomas), degenerative diseases (e.g., specific diagnosis of Parkinson disease), demyelinating diseases (e.g., assessment of normal-appearing tissue of multiple sclerosis), and cerebrovascular diseases (e.g., assessment of the microstructural environment of fresh infarctions). Representative metrics in clinical use are the full width at half maximum, also known as the mean displacement of the probability density function curve, which is derived from QSI, and diffusional kurtosis, which is derived from DKI. These new metrics may provide information on tissue structure in addition to that provided by conventional Gaussian DWI investigations that use the apparent diffusion coefficient and fractional anisotropy, recognized indices for evaluating disease and normal development in the brain and spine. In some clinical situations, sensitivity for detecting pathological conditions is higher using QSI and DKI than conventional DWI and diffusion tensor imaging (DTI) because DWI and DTI calculations are based on the assumption that water molecules follow a Gaussian distribution, whereas hindrance of the distribution of water molecules by complex and restricted structures in actual neural tissues produces distributions that are far from Gaussian. We review the technical aspects and clinical applications of QSI and DKI, focusing on clinical use and in vivo studies and highlighting differences from conventional diffusional metrics.