It has long been recognized that the diffusion tensor model is inappropriate to characterize complex fiber architecture, causing tensor‐derived measures such as the primary eigenvector and fractional anisotropy to be unreliable or misleading in these regions. There is however still debate about the impact of this problem in practice. A recent study using a Bayesian automatic relevance detection (ARD) multicompartment model suggested that a third of white matter (WM) voxels contain crossing fibers, a value that, whilst already significant, is likely to be an underestimate. The aim of this study is to provide more robust estimates of the proportion of affected voxels, the number of fiber orientations within each WM voxel, and the impact on tensor‐derived analyses, using large, high‐quality diffusion‐weighted data sets, with reconstruction parameters optimized specifically for this task. Two reconstruction algorithms were used: constrained spherical deconvolution (CSD), and the ARD method used in the previous study. We estimate the proportion of WM voxels containing crossing fibers to be ∼90% (using CSD) and 63% (using ARD). Both these values are much higher than previously reported, strongly suggesting that the diffusion tensor model is inadequate in the vast majority of WM regions. This has serious implications for downstream processing applications that depend on this model, particularly tractography, and the interpretation of anisotropy and radial/axial diffusivity measures. Hum Brain Mapp 34:2747–2766, 2013.

The ability of fiber tractography to delineate non‐invasively the white matter fiber pathways of the brain raises possibilities for clinical applications and offers enormous potential for neuroscience. In the last decade, fiber tracking has become the method of choice to investigate quantitative MRI parameters in specific bundles of white matter. For neurosurgeons, it is quickly becoming an invaluable tool for the planning of surgery, allowing for visualization and localization of important white matter pathways before and even during surgery. Fiber tracking has also claimed a central role in the field of “connectomics,” a technique that builds and studies comprehensive maps of the complex network of connections within the brain, and to which significant resources have been allocated worldwide. Despite its unique abilities and exciting applications, fiber tracking is not without controversy, in particular when it comes to its interpretation. As neuroscientists are eager to study the brain's connectivity, the quantification of tractography‐derived “connection strengths” between distant brain regions is becoming increasingly popular. However, this practice is often frowned upon by fiber‐tracking experts. In light of this controversy, this paper provides an overview of the key concepts of tractography, the technical considerations at play, and the different types of tractography algorithm, as well as the common misconceptions and mistakes that surround them. We also highlight the ongoing challenges related to fiber tracking. While recent methodological developments have vastly increased the biological accuracy of fiber tractograms, one should be aware that, even with state‐of‐the‐art techniques, many issues that severely bias the resulting structural “connectomes” remain unresolved.