The World Health Organization (WHO), in their 2022 report, identified cancer as one of the leading causes of death, accounting for about 16% of deaths worldwide. The Cancer-Moonshot community aims to reduce the cancer death rate by half in the next 25 years and wants to improve the lives of cancer-affected people. Cancer mortality can be reduced if detected early and treated appropriately. Cancers like breast cancer and cervical cancer have high cure probabilities when treated early in accordance with best practices. Integration of artificial intelligence (AI) into cancer research is currently addressing many of the challenges where medical experts fail to bring cancer to control and cure, and the outcomes are quite encouraging. AI offers many tools and platforms to facilitate more understanding and tackling of this life-threatening disease. AI-based systems can help pathologists in diagnosing cancer more accurately and consistently, reducing the case error rates. Predictive-AI models can estimate the likelihood for a person to get cancer by identifying the risk factors. Big data, together with AI, can enable medical experts to develop customized treatments for cancer patients. The side effects from this kind of customized therapy will be less severe in comparison with the generalized therapies. However, many of these AI tools will remain ineffective in fighting against cancer and saving the lives of millions of patients unless they are accessible and understandable to biologists, oncologists, and other medical cancer researchers. This paper presents the trends, challenges, and future directions of AI in cancer research. We hope that this paper will be of help to both medical experts and technical experts in getting a better understanding of the challenges and research opportunities in cancer diagnosis and treatment.