This special double issue of Measurement addresses a number of foundational issues in psychological measurement. It assembles three focus articles, with associated peer commentary, and replies by the authors. The first article challenges the routine assumption that psychometrics is a quantitative science; it argues that there may be no such thing as psychological measurement at all. The second article lays out a systematic framework for latent variable modeling that is intended to capture the notion of psychological measurement in its terms. The third article seeks to provide a conceptual distinction between theoretical variables that allow for an extension in possible worlds, and theoretical variables that do not. These focus articles are ...