Glaucoma is the leading cause of preventable, irreversible blindness world-wide. The disease can remain asymptomatic until severe, and an estimated 50%-90% of people with glaucoma remain undiagnosed. Thus, glaucoma screening is recommended for early detection and treatment. A cost-effective tool to detect glaucoma could expand healthcare access to a much larger patient population, but such a tool is currently unavailable. We trained a deep learning (DL) algorithm using a retrospective dataset of 58,033 images, assessed for gradability, glaucomatous optic nerve head (ONH) features, and referable glaucoma risk. The resultant algorithm was validated using 2 separate datasets. For referable glaucoma risk, the algorithm had an AUC of 0.940 (95%CI, 0.922-0.955) in validation dataset "A" (1,205 images, 1 image/patient; 19% referable where images were adjudicated by panels of fellowship-trained glaucoma specialists) and 0.858 (95% CI, 0.836-0.878) in validation dataset "B" (17,593 images from 9,643 patients; 9.2% referable where images were from the Atlanta Veterans Affairs Eye Clinic diabetic teleretinal screening program using clinical referral decisions as the reference standard). Additionally, we found that the presence of vertical cup-to-disc ratio >= 0.7, neuroretinal rim notching, retinal nerve fiber layer defect, and bared circumlinear vessels contributed most to referable glaucoma risk assessment by both glaucoma specialists and the algorithm. Algorithm AUCs ranged between 0.608-0.977 for glaucomatous ONH features. The DL algorithm was significantly more sensitive than 6 of 10 graders, including 2 of 3 glaucoma specialists, with comparable or higher specificity relative to all graders. A DL algorithm trained on fundus images alone can detect referable glaucoma risk with higher sensitivity and comparable specificity to eye care providers.