Due to recent advances in computer technology and the accessibility of large datasets, deep learning has become at the forefront of artificial intelligence and on various tasks, especially those related to image classification and modelling, its performance is often equal to or even better than human appreciation. Ophthalmology has always been in an ideal position to employ one of CNN’s most popular deep learning algorithms to evaluate vast volumes of data from these tests since it is one of the health practices that focuses extensively on imaging. Glaucoma is one among the situations in which CNN can benefit from the enormous quantity of data collected by tests that assess the anatomy as well as function of the optic nerve and macula. We discussed the recommended use of CNN algorithm for specific glaucoma scenarios, such as fundus photography screening and diagnosis and detection of the course of glaucoma through OCT imaging modality. The purpose of this article is not only to critically examine and discuss the latest applications of CNN models in glaucoma but also to focus on the challenges associated with developing such models for screening, diagnosis, and progress detection. After a brief overview of the clinical practices and their comparison with conventional clinical methods, we discussed training and validation of CNN algorithm and how it was developed and why it is particularly suitable for glaucoma. The following features make our contribution worthwhile and unique among the reviews of similar kind: (i) our review classifies the existing literature with respect to detection of the glaucoma disease using conventional and nonconventional approaches; (ii) it covers a very different outlook of the glaucoma disease by providing in-depth discussions of the existing works at different granularity levels, that is, from primary to mediatory to the severe level; (iii) this state-of-the-art review covers each article in the following dimensions: the computer-based approach to tomographic model; analysis of different datasets; and summarizing the literature review in a disciplined way by mentioning the research gap concluded with discussion on future work.