Deep learning (DL) models in general and convolutional neural networks (CNN) in particular, have rapidly turned out to be methodologies of interest for applications concerned with analysing medical images for classification of different types of disc abnormalities to avoid false outcomes in diagnosis and to automate the domain to a greater extent. In this paper, a detailed review has been conducted on how different state-of-the-art DL methodologies have been applied on disc disease diagnosis by using various medical imaging modalities. It focuses on how to maximize the decision analysis in disease diagnosis in terms of five different aspects, such as types of medical imaging modalities used, datasets and their available categories, pre-processing techniques, various DL models, and performance metrics used for disc degenerative disease (DDD) classification. Further, this study outlines quantitative, qualitative, and critical analysis of the five objectives. amongst the selected studies most of them used a pre-trained model or constructed a new DL model to classify DDD. Finally, this review outlines eight open challenges for researchers who are interested in DDD classification models. This review study will enhance the knowledge domain of researchers and will also provide a comprehensive insight of the effectiveness of the DL techniques being employed in medical diagnosis of DDD.