Fiber tractography based on non-invasive diffusion imaging is at the heart of connectivity studies of the human brain. To date, the approach has not been systematically validated in ground truth studies. Based on a simulated human brain dataset with ground truth white matter tracts, we organized an open international tractography challenge, which resulted in 96 distinct submissions from 20 research groups. While most state-of-the-art algorithms reconstructed 90% of ground truth bundles to at least some extent, on average they produced four times more invalid than valid bundles. About half of the invalid bundles occurred systematically in the majority of submissions. Our results demonstrate fundamental ambiguities inherent to tract reconstruction methods based on diffusion orientation information, with critical consequences for the approach of diffusion tractography in particular and human connectivity studies in general.