Given the enormous output and pace of development of artificial intelligence (AI) methods in medical imaging, it can be challenging to identify the true success stories to determine the state-of-the-art of the field. This report seeks to provide the magnetic resonance imaging (MRI) community with an initial guide into the major areas in which the methods of AI are contributing to MRI in oncology. After a general introduction to artificial intelligence, we proceed to discuss the successes and current limitations of AI in MRI when used for image acquisition, reconstruction, registration, and segmentation, as well as its utility for assisting in diagnostic and prognostic settings. Within each section, we attempt to present a balanced summary by first presenting common techniques, state of readiness, current clinical needs, and barriers to practical deployment in the clinical setting. We conclude by presenting areas in which new advances must be realized to address questions regarding generalizability, quality assurance and control, and uncertainty quantification when applying MRI to cancer to maintain patient safety and practical utility.