Machine learning techniques have great potential to improve medical diagnostics, offering ways to improve accuracy, reproducibility and speed, and to ease workloads for clinicians. In the field of histopathology, deep learning algorithms have been developed that perform similarly to trained pathologists for tasks such as tumor detection and grading. However, despite these promising results, very few algorithms have reached clinical implementation, challenging the balance between hope and hype for these new techniques. This Review provides an overview of the current state of the field, as well as describing the challenges that still need to be addressed before artificial intelligence in histopathology can achieve clinical value.