We propose Iterative Homography Network, namely IHN, a new deep homography estimation architecture. Different from previous works that achieve iterative refinement by network cascading or untrainable IC-LK iterator, the iterator of IHN has tied weights and is completely trainable. IHN achieves state-of-the-art accuracy on several datasets including challenging scenes. We propose 2 versions of IHN: (1) IHN for static scenes, (2) IHN-mov for dynamic scenes with moving objects. Both versions can be arranged in 1-scale for efficiency or 2-scale for accuracy. We show that the basic 1-scale IHN already outperforms most of the existing methods. On a variety of datasets, the 2-scale IHN outperforms all competitors by a large gap. We introduce IHN-mov by producing an inlier mask to further improve the estimation accuracy of moving-objects scenes. We experimentally show that the iterative framework of IHN can achieve 95% error reduction while considerably saving network parameters. When processing sequential image pairs, IHN can achieve 32.7 fps, which is about 8× the speed of IC-LK iterator. Source code is available at https://github.com/imdumpl78/IHN .