A fovea is a pitted invagination in the inner retinal tissue (fovea interna) that overlies an area of photoreceptors specialized for high acuity vision (fovea externa). Although the shape of the vertebrate fovea varies considerably among the species, there are two basic types. The retina of many predatory fish, reptilians, and birds possess one (or two) convexiclivate fovea(s), while the retina of higher primates contains a concaviclivate fovea. By refraction of the incoming light, the convexiclivate fovea may function as image enlarger, focus indicator, and movement detector. By centrifugal displacement of the inner retinal layers, which increases the transparency of the central foveal tissue (the foveola), the primate fovea interna improves the quality of the image received by the central photoreceptors. In this review, we summarize ‒ with the focus on Müller cells of the human and macaque fovea ‒ data regarding the structure of the primate fovea, discuss various aspects of the optical function of the fovea, and propose a model of foveal development. The "Müller cell cone" of the foveola comprises specialized Müller cells which do not support neuronal activity but may serve optical and structural functions. In addition to the "Müller cell cone", structural stabilization of the foveal morphology may be provided by the 'z-shaped' Müller cells of the fovea walls, via exerting tractional forces onto Henle fibers. The spatial distribution of glial fibrillary acidic protein may suggest that the foveola and the Henle fiber layer are subjects to mechanical stress. During development, the foveal pit is proposed to be formed by a vertical contraction of the centralmost Müller cells. After widening of the foveal pit likely mediated by retracting astrocytes, Henle fibers are formed by horizontal contraction of Müller cell processes in the outer plexiform layer and the centripetal displacement of photoreceptors. A better understanding of the molecular, cellular, and mechanical factors involved in the developmental morphogenesis and the structural stabilization of the fovea may help to explain the (patho-) genesis of foveal hypoplasia and macular holes.