Objective: Skin diseases constitute a widespread health concern, and the application of machine learning and deep learning algorithms has been instrumental in improving diagnostic accuracy and treatment effectiveness. This paper aims to provide a comprehensive review of the existing research on the utilization of machine learning and deep learning in the field of skin disease diagnosis, with a particular focus on recent widely used methods of deep learning. The present challenges and constraints were also analyzed and possible solutions were proposed. Methods: We collected comprehensive works from the literature, sourced from distinguished databases including IEEE, Springer, Web of Science, and PubMed, with a particular emphasis on the most recent 5-year advancements. From the extensive corpus of available research, twenty-nine articles relevant to the segmentation of dermatological images and forty-five articles about the classification of dermatological images were incorporated into this review. These articles were systematically categorized into two classes based on the computational algorithms utilized: traditional machine learning algorithms and deep learning algorithms. An in-depth comparative analysis was carried out, based on the employed methodologies and their corresponding outcomes. Conclusions: Present outcomes of research highlight the enhanced effectiveness of deep learning methods over traditional machine learning techniques in the field of dermatological diagnosis. Nevertheless, there remains significant scope for improvement, especially in improving the accuracy of algorithms. The challenges associated with the availability of diverse datasets, the generalizability of segmentation and classification models, and the interpretability of models also continue to be pressing issues. Moreover, the focus of future research should be appropriately shifted. A significant amount of existing research is primarily focused on melanoma, and consequently there is a need to broaden the field of pigmented dermatology research in the future. These insights not only emphasize the potential of deep learning in dermatological diagnosis but also highlight directions that should be focused on.