Advancements in AI have notably changed cancer research, improving patient care by enhancing detection, survival prediction, and treatment efficacy. This review covers the role of Machine Learning, Soft Computing, and Deep Learning in oncology, explaining key concepts and algorithms (like SVM, Naïve Bayes, and CNN) in a clear, accessible manner. It aims to make AI advancements understandable to a broad audience, focusing on their application in diagnosing, classifying, and predicting various cancer types, thereby underlining AI's potential to better patient outcomes. Moreover, we present a tabular summary of the most significant advances from the literature, offering a time-saving resource for readers to grasp each study's main contributions. The remarkable benefits of AI-powered algorithms in cancer care underscore their potential for advancing cancer research and clinical practice. This review is a valuable resource for researchers and clinicians interested in the transformative implications of AI in cancer care.