Vector representations of words are commonly used to give language models a basic understanding of a domain’s vocabulary, and various techniques have been developed to build good such representations from a text corpus, a knowledge graph, or an ontology. In this talk, I will talk about such representations and what it means for a such a representation to faithfully represent the relationships between concepts, individuals, and relations from an ontology. In particular, I will explain how representing concepts as n-dimensional spaces - rather than points in an n-dimensional space - will allow us to interpret subsumption between concepts as containment of their respective spaces. And I will discuss various approaches and their properties.