Many developmental processes, such as plasticity and aging, or pathological processes such as neurological diseases are characterized by modulations of specific cellular types and their microstructures. Diffusion-weighted Magnetic Resonance Imaging (DW-MRI) is a powerful technique for probing microstructure, yet its information arises from the ubiquitous, non-specific water signal. By contrast, diffusion-weighted Magnetic Resonance Spectroscopy (DW-MRS) allows specific characterizations of tissues such as brain and muscle in vivo by quantifying the diffusion properties of MR-observable metabolites. Many brain metabolites are predominantly intracellular, and some of them are preferentially localized in specific brain cell populations, e.g., neurons and glia. Given the microstructural sensitivity of diffusion-encoding filters, investigation of metabolite diffusion properties using DW-MRS can thus provide exclusive cell and compartment-specific information. Furthermore, since many models and assumptions are used for quantification of water diffusion, metabolite diffusion may serve to generate a-priori information for model selection in DW-MRI. However, DW-MRS measurements are extremely challenging, from the acquisition to the accurate and correct analysis and quantification stages. In this review, we survey the state-of-the-art methods that have been developed for the robust acquisition, quantification and analysis of DW-MRS data and discuss the potential relevance of DW-MRS for elucidating brain microstructure in vivo. The review highlights that when accurate data on the diffusion of multiple metabolites is combined with accurate computational and geometrical modeling, DW-MRS can provide unique cell-specific information on the intracellular structure of brain tissue, in health and disease, which could serve as incentives for further application in vivo in human research and clinical MRI.