Today, a plethora of model-based diffusion MRI (dMRI) techniques exist that aim to provide quantitative metrics of cellular-scale tissue properties. In the brain, many of these techniques focus on cylindrical projections such as axons and dendrites. Capturing additional tissue features is challenging, as conventional dMRI measurements have limited sensitivity to different cellular components, and modelling cellular architecture is not trivial in heterogeneous tissues such as grey matter. Additionally, fitting complex non-linear models with traditional techniques can be time-consuming and prone to local minima, which hampers their widespread use. In this thesis, we harness recent advances in measurement technology and modelling efforts to tackle these challenges. We probe the utility of B-tensor encoding, a technique that offers additional sensitivity to tissue microstructure compared to conventional measurements, and observe that B-tensor encoding provides unique contrast in grey matter. Motivated by this and recent work showing that the diffusion signature of soma in grey matter may be captured with spherical compartments, we use B-tensor encoding measurements and a biophysical model to disentangle spherical and cylindrical cellular structures. We map apparent markers of these geometries in healthy human subjects and evaluate the extent to which they may be interpreted as correlates of soma and projections. To ensure fast and robust model fitting, we use supervised machine learning (ML) to estimate parameters. We explore limitations in ML fitting in several microstructure models, including the model developed here, and demonstrate that the choice of training data significantly impacts estimation performance. We highlight that high precision obtained using ML may mask strong biases and that visual assessment of the parameter maps is not sufficient for evaluating the quality of the estimates. We believe that the methods developed in this work provide new insight into the reliability and potential utility of advanced dMRI and ML in microstructure imaging.