Diabetic retinopathy (DR) is an eye disease that is caused by damage of blood vessels in the retina due to excess sugar level. DR is a severe problem that might lead to blindness among working age people if not detected in time. As per the WHO report, in 2016, diabetes was the main reason of 1.6 million deaths. Between 2000 and 2016, there was an increment of 5% in premature deaths due to diabetes. Thus, early diagnosis of DR is desirable to safeguard human beings from the severity of DR. Analysis of blood vessel structures in retinal fundus images play a vital role in ophthalmology. However, it is challenging to perform manual analysis of the retinal fundus images by the medical fraternity as it is time-consuming, expensive, and tedious. The blood vessel structure includes variation in the size of the vessels, branching patterns, appearance, changes in thickness, etc. Many machine learning and deep learning-based automated techniques have been proposed for analyzing and detecting blood vessel structures for determining DR classification. The proposed paper aims at discussing and comparing automated processes for predicting various stages of DR by reviewing prominent and novel papers in the field of automatic classification of DR. Even though the field of automatic classification of retinal fundus images has progressed a lot, there are still some shortcomings or lacunas which need to be addressed.