In 2011, the editors of this volume convened 64 researchers in mathematics education and psychometrics to promote collaboration around the measurement of constructs relevant to mathematics education. This monograph codifies much of the knowledge shared during that conference with the purpose of informing mathematics education researchers about psychometric models that can address a wide range of research questions. The underlying premise is that many mathematics educators use and work with measurement but are potentially limited in their work if they do not understand its nuances.