Although the visual system extends through the brain, most vision loss originates from defects in the eye. Its central element is the neural retina, which senses light, processes visual signals, and transmits them to the rest of the brain through the optic nerve (ON). Surrounding the retina are numerous other structures, conventionally divided into anterior and posterior segments. Here we used high-throughput single nucleus RNA sequencing (snRNA-seq) to classify and characterize cells in the extraretinal components of the posterior segment: ON, optic nerve head (ONH), peripheral sclera, peripapillary sclera (PPS), choroid, and retinal pigment epithelium (RPE). Defects in each of these tissues are associated with blinding diseases - for example, glaucoma (ONH and PPS), optic neuritis (ON), retinitis pigmentosa (RPE), and age-related macular degeneration (RPE and choroid). From ∼151,000 single nuclei, we identified 37 transcriptomically distinct cell types, including multiple types of astrocytes, oligodendrocytes, fibroblasts, and vascular endothelial cells. Our analyses revealed a differential distribution of many cell types among distinct structures. Together with our previous analyses of the anterior segment and retina, the new data complete a "Version 1" cell atlas of the human eye. We used this atlas to map the expression of >180 genes associated with the risk of developing glaucoma, which is known to involve ocular tissues in both anterior and posterior segments as well as neural retina. Similar methods can be used to investigate numerous additional ocular diseases, many of which are currently untreatable.