Deep learning models are applied seamlessly across various computer vision tasks like object detection, object tracking, scene understanding and further. The application of cutting-edge deep learning (DL) models like U-Net in the classification and segmentation of medical images on different modalities has established significant results in the past few years. Ocular diseases like Diabetic Retinopathy (DR), Glaucoma, Age-Related Macular Degeneration (AMD / ARMD), Hypertensive Retina (HR), Cataract, and dry eyes can be detected at the early stages of disease onset by capturing the fundus image or the anterior image of the subject’s eye. Early detection is key to seeking early treatment and thereby preventing the disease progression, which in some cases may lead to blindness. There is a plethora of deep learning models available which have established significant results in medical image processing and specifically in ocular disease detection. A given task can be solved by using a variety of models and or a combination of them. Deep learning models can be computationally expensive and deploying them on an edge device may be a challenge. This paper provides a comprehensive report and critical evaluation of the various deep learning architectures that can be used to segment and classify ocular diseases namely Glaucoma and Hypertensive Retina on the posterior images of the eye. This review also compares the models based on complexity and edge deployability.