Gender inclusivity in language has become a central topic of debate and research. Its application in the cross-lingual contexts of human and machine translation (MT), however, remains largely unexplored. Here, we discuss Gender-Neutral Translation (GNT) as a form of gender inclusivity in translation and advocate for its adoption for MT models, which have been found to perpetuate gender bias and discrimination. To this aim, we review a selection of relevant institutional guidelines for Gender-Inclusive Language (GIL) to collect and systematize useful strategies of gender neutralization. Then, we discuss GNT and its scenarios of use, devising a list of desiderata. Finally, we identify the main technical challenges to the implementation of GNT in MT. Throughout these contributions we focus on translation from English into Italian, as representative of salient linguistic transfer problems, due to the different rules for gender marking in their grammar.