This chapter presents an overview of advances in diffusion MRI devised to probe and quantify increasingly subtle features of the microstructure of a biological tissue. The first two sections cover popular models that aim to overcome the shortcomings of DTI. These are categorised as (1) signal models, which capture the variations in the diffusion signal to draw inferences about the tissue, and (2) biophysical models, which aim to estimate actual microstructural tissue properties that influence the signal. The next section provides a list of popular software packages useful for advanced dMRI modelling. The last section is dedicated to current and future trends in acquisition, robust parameter estimation, hardware advances and multi-modal imaging. These provide a flavour of the next-generation diffusion MRI technologies.