The importance of studying the brain microstructure is described and the existing and state of the art non-invasive methods for the investigation of the brain microstructure using Diffusion Weighted Magnetic Resonance Imaging (DWI) is studied. In the next step, Cramer-Rao Lower Bound (CRLB) analysis is described and utilised for assessment of the minimum estimation error and uncertainty level of different Diffusion Weighted Magnetic Resonance (DWMR) signal decay models. The analyses are performed considering the best scenario through which, we assume that the models are the appropriate representation of the measured phenomena. This includes the study of the sensitivity of the estimations to the measurement and model parameters. It is demonstrated that none of the existing models can achieve a reasonable minimum uncertainty level under typical measurement setup. At the end, the practical obstacles for achieving higher performance in clinical and experimental environments are studied and their effects on feasibility of the methods are discussed.