In this paper, we apply different NMT models to the problem of historical spelling normalization for five languages: English, German, Hungarian, Icelandic, and Swedish. The NMT models are at different levels, have different attention mechanisms, and different neural network architectures. Our results show that NMT models are much better than SMT models in terms of character error rate. The vanilla RNNs are competitive to GRUs/LSTMs in historical spelling normalization. Transformer models perform better only when provided with more training data. We also find that subword-level models with a small subword vocabulary are better than character-level models. In addition, we propose a hybrid method which further improves the performance of historical spelling normalization.