Existentialism is a well-known and historically delimited intellectual movement that includes a recognisable group of mid-twentieth-century figures, including Heidegger, Sartre, Levinas, De Beauvoir, Fanon, Merleau-Ponty amongst others, drawing on nineteenth-century forerunners such as Kierkegaard, Emerson and Nietzsche. These are undoubtedly touchstones for thinking about what an existential enquiry consists in. For the editors of this volume, though, existential enquiry engages a theme that is narrower and more universal. This might be framed as a question: How to understand the irreducible living breathing human individual who is both a subject and an object in its own world, and whose life cannot be replaced with the lives of the other human beings around it? Existential enquiry begins, then, at the point when it reasserts a truth about life as any actually existing person experiences it; that, whatever shape subjectivity may take in its social networks, or in cultural discourse viewed from outside, each life is and remains distinct to itself, unique, finite and irreplaceable. If, then, existential enquiry is, or should be, a ‘tale of the richness of being versus abstraction’ what kind of language of observation and analysis does the enquirer need to tell it? The editors review the options.