Research into artificial intelligence (AI) has made tremendous progress over the past decade. In particular, the AI-powered analysis of images and signals has reached human-level performance in many applications owing to the efficiency of modern machine learning methods, in particular deep learning using convolutional neural networks. Research into the application of AI to medical imaging is now very active, especially in the field of cardiovascular imaging because of the challenges associated with acquiring and analysing images of this dynamic organ. In this Review, we discuss the clinical questions in cardiovascular imaging that AI can be used to address and the principal methodological AI approaches that have been developed to solve the related image analysis problems. Some approaches are purely data-driven and rely mainly on statistical associations, whereas others integrate anatomical and physiological information through additional statistical, geometric and biophysical models of the human heart. In a structured manner, we provide representative examples of each of these approaches, with particular attention to the underlying computational imaging challenges. Finally, we discuss the remaining limitations of AI approaches in cardiovascular imaging (such as generalizability and explainability) and how they can be overcome.