Automatic Non-rigid Histological Image Registration (ANHIR) challenge was organized to compare the performance of image registration algorithms on several kinds of microscopy histology images in a fair and independent manner. We have assembled 8 datasets, containing 355 images with 18 different stains, resulting in 481 image pairs to be registered. Registration accuracy was evaluated using manually placed landmarks. In total, 256 teams registered for the challenge, 10 submitted the results, and 6 participated in the workshop. Here, we present the results of 7 well-performing methods from the challenge together with 6 well-known existing methods. The best methods used coarse but robust initial alignment, followed by non-rigid registration, used multiresolution, and were carefully tuned for the data at hand. They outperformed off-the-shelf methods, mostly by being more robust. The best methods could successfully register over 98% of all landmarks and their mean landmark registration accuracy (TRE) was 0.44% of the image diagonal. The challenge remains open to submissions and all images are available for download.