The main difference between artificial intelligence (AI) systems and simple automated algorithms is the ability to learn, synthesize and conclude. The AI system is trained on a set of examples, including pictures, characteristics of patients with a certain disease, then it allows to generalize a lot of such examples and get some general functional dependence, which brings in line the patient data and a certain diagnosis. The system can be named intelligent if this synthetizing ability is realized. Although the AI systems are now becoming more understood and accepted by doctors, a deeper understanding of «how it works» is needed. The article provides a detailed review of the application of methods and models of artificial intelligence in the diagnostics of cancer based on the of multimodal instrumental data. The basic concepts of artificial intelligence and directions of its development are presented. From the point of view of data processing, the stages of development of AI systems are identical. The stages of intellectual processing of diagnostic data are considered in the paper. They include the acquisition and use of training databases of oncological diseases, pre-processing of images, segmentation to highlight the studied objects of diagnosis and classification of these objects to determine whether they are malignant or benign. One of the problems limiting the acceptance of AI systems development by the medical community is the imperfection of the explainability of the results obtained by intelligent systems. Authors pay attention to importance of the development of so-called explanatory intelligence, because its absence currently significantly inhibits the introduction and use of intelligent diagnostic systems in medicine. In addition, the purpose of the article is a way to develop the interaction between a radiologists and data scientists.