Since its introduction in the early 1990s, diffusion-weighted magnetic resonance imaging (MRI) has played a crucial role in the non-invasive evaluation of tissue microstructure of brain parenchyma in vivo. Diffusion anisotropy, in particular, has been extensively used to infer histological changes due to brain maturation and pathology, as it shows a clear dependence on tissue architecture. Although the resolution used in most studies lies in the macroscopic range, the information provided originates at the microscopic level and, as such, diffusion MRI serves as a microscope that can reveal profound details of tissue with direct clinical and research applications. The interpretation of diffusion parameters of white matter rests on what is known to drive diffusion anisotropy, namely axonal membranes, density and coherence, as well as myelin sheaths. However, these factors interact to modulate anisotropy, making interpretations potentially difficult. While there are numerous publications that report diffusion changes in response to particular, histologically confirmed tissue abnormalities in animal models of disease, the microscopic correlates of altered diffusion parameters due to neurological disorders in humans have been difficult to characterize. Animal models may provide insight into the mechanisms involved, but do not necessarily provide accurate representations of the human condition, making human diffusion MRI studies with direct histological confirmation crucial for our understanding of tissue changes secondary to neurodevelopment and disease. This work provides a synopsis of tissue characteristics that give rise to highly informative, specific diffusion patterns, but also of how methodological and artifactual aspects can provide erroneous diffusion measurements that do not accurately reflect tissue and may lead to misinterpretation of results. Examples of diffusion changes due to human conditions are provided to illustrate the wealth of applications of diffusion MRI in clinical and research fields.