Primates can recognize faces across a range of viewing conditions. Representations of individual identity should thus exist that are invariant to accidental image transformations like view direction. We targeted the recently discovered face-processing network of the macaque monkey that consists of six interconnected face-selective regions and recorded from the two middle patches (ML, middle lateral, and MF, middle fundus) and two anterior patches (AL, anterior lateral, and AM, anterior medial). We found that the anatomical position of a face patch was associated with a unique functional identity: Face patches differed qualitatively in how they represented identity across head orientations. Neurons in ML and MF were view-specific; neurons in AL were tuned to identity mirror-symmetrically across views, thus achieving partial view invariance; and neurons in AM, the most anterior face patch, achieved almost full view invariance.