With language technology increasingly affecting individuals’ lives, many recent works have investigated the ethical aspects of NLP. Among other topics, researchers focused on the notion of morality, investigating, for example, which moral judgements language models make. However, there has been little to no discussion of the terminology and the theories underpinning those efforts and their implications. This lack is highly problematic, as it hides the works’ underlying assumptions and hinders a thorough and targeted scientific debate of morality in NLP. In this work, we address this research gap by (a) providing an overview of some important ethical concepts stemming from philosophy and (b) systematically surveying the existing literature on moral NLP w.r.t. their philosophical foundation, terminology, and data basis. For instance, we analyse what ethical theory an approach is based on, how this decision is justified, and what implications it entails. Our findings surveying 92 papers show that, for instance, most papers neither provide a clear definition of the terms they use nor adhere to definitions from philosophy. Finally, (c) we give three recommendations for future research in the field. We hope our work will lead to a more informed, careful, and sound discussion of morality in language technology.