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Word alignments identify translational correspondences between words in a parallel sentence pair and is used, for instance, to learn bilingual dictionaries, to train statistical machine translation systems, or to perform quality estimation. In most areas of natural lan- guage processing, neural network models nowadays constitute the preferred approach, a situation that might also apply to word align- ment models. In this work, we study and comprehensively evaluate neural models for unsupervised word alignment for four language pairs, contrasting several variants of neural models. We show that in most settings, neural versions of the IBM-1 and hidden Markov models vastly outperform their discrete counterparts. We also analyze typical alignment errors of the baselines that our models over- come to illustrate the benefits — and the limitations — of these new models for morphologically rich languages.