The advent of deep learning has engendered renewed and rapidly growing interest in artificial intelligence (AI) in radiology to analyze images, manipulate textual reports, and plan interventions. Applications of deep learning and other AI approaches must be guided by sound medical knowledge to assure that they are developed successfully and that they address important problems in biomedical research or patient care. To date, AI has been applied to a limited number of real-world radiology applications. As AI systems become more pervasive and are applied more broadly, they will benefit from medical knowledge on a larger scale, such as that available through computer-based approaches. A key approach to represent computer-based knowledge in a particular domain is an ontology. As defined in informatics, an ontology defines a domain's terms through their relationships with other terms in the ontology. Those relationships, then, define the terms' semantics, or "meaning." Biomedical ontologies commonly define the relationships between terms and more general terms, and can express causal, part-whole, and anatomic relationships. Ontologies express knowledge in a form that is both human-readable and machinecomputable. Some ontologies, such as RSNA's RadLex radiology lexicon, have been applied to applications in clinical practice and research, and may be familiar to many radiologists. This article describes how ontologies can support research and guide emerging applications of AI in radiology, including natural language processing, image-based machine learning, radiomics, and planning.