In 2016, Goeffrey Hinton, the Godfather of Machine Learning, predicted that we should stop training radiologists, as within five years deep learning would do better than radiologists at interpreting medical images. Five years later, deep learning in nowhere close to replacing radiologists. Some systems have been designed to perform a single diagnosis almost as well as radiologists on very limited datasets, but they are nowhere close to replacing radiologists. In this talk, given by a radiologist, who has a PhD in Artificial Intelligence, we will look at the promise and challenges in the application of artificial intelligence to the task of interpreting medical images, and how future AI systems might help simplify the work of radiologists rather that fully replace them.