Cancer is an aggressive disease with a low median survival rate. Ironically, the treatment process is long and very costly due to its high recurrence and mortality rates. Accurate early diagnosis and prognosis prediction of cancer are essential to enhance the patient's survival rate. Developments in statistics and computer engineering over the years have encouraged many scientists to apply computational methods such as multivariate statistical analysis to analyze the prognosis of the disease, and the accuracy of such analyses is significantly higher than that of empirical predictions. Furthermore, as artificial intelligence (AI), especially machine learning and deep learning, has found popular applications in clinical cancer research in recent years, cancer prediction performance has reached new heights. This article reviews the literature on the application of AI to cancer diagnosis and prognosis, and summarizes its advantages. We explore how AI assists cancer diagnosis and prognosis, specifically with regard to its unprecedented accuracy, which is even higher than that of general statistical applications in oncology. We also demonstrate ways in which these methods are advancing the field. Finally, opportunities and challenges in the clinical implementation of AI are discussed. Hence, this article provides a new perspective on how AI technology can help improve cancer diagnosis and prognosis, and continue improving human health in the future.