Skin cancer continues to remain one of the major healthcare issues across the globe. If diagnosed early, skin cancer can be treated successfully. While early diagnosis is paramount for an effective cure for cancer, the current process requires the involvement of skin cancer specialists, which makes it an expensive procedure and not easily available and affordable in developing countries. This dearth of skin cancer specialists has given rise to the need to develop automated diagnosis systems. In this context, Artificial Intelligence (AI)-based methods have been proposed. These systems can assist in the early detection of skin cancer and can consequently lower its morbidity, and, in turn, alleviate the mortality rate associated with it. Machine learning and deep learning are branches of AI that deal with statistical modeling and inference, which progressively learn from data fed into them to predict desired objectives and characteristics. This survey focuses on Machine Learning and Deep Learning techniques deployed in the field of skin cancer diagnosis, while maintaining a balance between both techniques. A comparison is made to widely used datasets and prevalent review papers, discussing automated skin cancer diagnosis. The study also discusses the insights and lessons yielded by the prior works. The survey culminates with future direction and scope, which will subsequently help in addressing the challenges faced within automated skin cancer diagnosis.