In contrast to conventional diffusion magnetic resonance imaging (MRI), multi-b-value diffusion MRI methods are able to separate the signal from free water, pseudo-diffusion, and non-Gaussian components of water molecule diffusion. These approaches can then be utilised in so-called intravoxel incoherent motion imaging and diffusion kurtosis imaging. Various parameters provided by these methods can describe additional characteristics of the tissue microstructure and potentially help in the diagnosis and classification of various pathological processes. In this review, we present the basic principles and methods of analysing multi-b-value diffusion imaging data and specifically focus on the known possibilities for its use in the diagnosis of brain lesions. We also suggest possible directions for further research.