The retina fundus images are critical diagnostic tools for the early detection of ophthalmic problems. Prompt diagnosis and treatment of eye-related problems are important to prevent blindness or vision loss. Recently, CNN algorithms have become effective in tasks relating to recognition, delineation, and classification. Therefore we propose a review to summarize different CNN algorithms for segmenting and classifying retinal fundus images. This review systematically searches different repositories for methods that use CNN for the segmentation and classification of retinal fundus images. A thorough screening of abstracts and titles to ascertain their relevance was done. A total of fifty-two studies were included in our review, with content such as database usage, disadvantages, and advantages. A comparison of two accuracies was also carried out with a graph depicting database usage. Important insights, limitations, observations, and future directions were elucidated. Finally, findings suggest that CNN algorithms produce good accuracies despite their limitations.