Nowadays, one of the key indicators that have a great impact on the evolution of society is artificial intelligence. AI and Big Data technologies are widely used to analyze biomedical data. This article describes what artificial intelligence and Big Data are and what are the modern possibilities of using their methods and technologies. The statistics showing the growth in the use of Big Data and AI technologies in medical research are presented. The main types of artificial neural networks used in this area are considered, as well as examples of the successful use of Big Data technologies in medicine. The effectiveness of the use of special computer programs in the field of health care, which allows detecting diseases at early stages, are demonstrated. The key technological and ethical problems of introducing artificial intelligence technologies into medicine are considered, the difficulties of implementation, integration and dissemination of technologies are shown. Special attention is paid to the use of AI in the fight against the global pandemic, the Covid-19 coronavirus infection. The methods of using AI in various countries for collecting data, analyzing and then building a model of the spread and mutation of coronavirus under various scenarios of the development of the situation and the introduction of special restrictive measures, as well as predicting their effectiveness are analyzed.