Recent years have seen an increasing need for gender-neutral and inclusive language. Within the field of NLP, there are various mono- and bilingual use cases where gender inclusive language is appropriate, if not preferred due to ambiguity or uncertainty in terms of the gender of referents. In this work, we present a rule-based and a neural approach to gender-neutral rewriting for English along with manually curated synthetic data (WinoBias+) and natural data (OpenSubtitles and Reddit) benchmarks. A detailed manual and automatic evaluation highlights how our NeuTral Rewriter, trained on data generated by the rule-based approach, obtains word error rates (WER) below 0.18% on synthetic, in-domain and out-domain test sets.