Quantification of cerebral white matter hyperintensities (WMH) of presumed vascular origin is of key importance in many neurological research studies. Currently, measurements are often still obtained from manual segmentations on brain MR images, which is a laborious procedure. Automatic WMH segmentation methods exist, but a standardized comparison of the performance of such methods is lacking. We organized a scientific challenge, in which developers could evaluate their method on a standardized multi-center/-scanner image dataset, giving an objective comparison: the WMH Segmentation Challenge (https://wmh.isi.uu.nl/). Sixty T1+FLAIR images from three MR scanners were released with manual WMH segmentations for training. A test set of 110 images from five MR scanners was used for evaluation. Segmentation methods had to be containerized and submitted to the challenge organizers. Five evaluation metrics were used to rank the methods: (1) Dice similarity coefficient, (2) modified Hausdorff distance (95th percentile), (3) absolute log-transformed volume difference, (4) sensitivity for detecting individual lesions, and (5) F1-score for individual lesions. Additionally, methods were ranked on their inter-scanner robustness. Twenty participants submitted their method for evaluation. This paper provides a detailed analysis of the results. In brief, there is a cluster of four methods that rank significantly better than the other methods, with one clear winner. The inter-scanner robustness ranking shows that not all methods generalize to unseen scanners. The challenge remains open for future submissions and provides a public platform for method evaluation.