The visual comparison of unfamiliar faces—or ‘face matching’—is utilized widely for person identification in applied settings and has generated substantial research interest in psychology, but a cognitive theory to explain how observers perform this task does not exist. This chapter outlines issues of importance to support the development of a cognitive account of unfamiliar face matching. Characteristics of the face, such as within-person variability and between-person similarity in appearance, are considered as the visual input upon which identification must build. The cognitive mechanisms that observers may bring to bear on faces during identity comparison are analysed, focusing on attention, perception, evaluation, and decision processes, including sources of individual differences at each of these stages. Finally, the role of different experimental and occupational contexts in understanding face matching and for optimizing theory development is discussed.