To process language in a way that is compatible with human expectations in a communicative interaction, we need computational representations of lexical properties that form the basis of human knowledge of words. In this article, we concentrate on word-level semantics. We discuss key concepts and issues that underlie the scientific understanding of the human lexicon: its richly structured semantic representations, their ready and continual adaptability, and their grounding in crosslinguistically valid conceptualization. We assess the state of the art in natural language processing (NLP) in achieving these identified properties, and suggest ways in which the language sciences can inspire new approaches to their computational instantiation.