The micro-architecture of brain tissue obstructs the movement of diffusing water molecules, causing tissue-dependent, often anisotropic diffusion profiles. In diffusion MRI (dMRI), the relation between brain tissue structure and diffusion anisotropy is studied using oriented diffusion gradients, resulting in tissue-and orientation-dependent diffusion-weighted images (DWIs). Over time, various methods have been proposed that summarize these DWIs, that can be measured at different orientations, gradient strengths and diffusion times into one " diffusion anisotropy " measure. This book chapter is dedicated to understanding the similarities and differences between the diffusion anisotropy metrics that different methods estimate. We first discuss the physical interpretation of diffusion anisotropy in terms of the diffusion properties around nervous tissue. We then explain how DWIs are influenced by diffusion anisotropy and the parameters of the dMRI acquisition itself. We then go through the state-of-the-art of signal-based and multi-compartment-based dMRI methods that estimate diffusion anisotropy-related methods, focusing on their limitations and applications. We finally discuss confounding factors in the estimation of diffusion anisotropy and current challenges.