Deep-learning-based tomographic imaging is an important application of artificial intelligence and a new frontier of machine learning. Deep learning has been widely used in computer vision and image analysis, which deal with existing images, improve these images, and produce features from them. Since 2016, deep learning techniques have been actively researched for tomographic imaging, especially in the context of biomedicine, with impressive results and great potential. Tomographic reconstruction produces images of multi-dimensional structures from externally measured ‘encoded’data in the form of various tomographic transforms (integrals, harmonics, echoes and so on). In this Review, we provide a general background, highlight representative results with an emphasis on medical imaging, and discuss key issues that need to be addressed in this emerging field. In particular, tomographic imaging is an integral part of modern medicine, and will play a key role in personalized, preventive and precision medicine and make it intelligent, inexpensive and indiscriminate.