Deep learning is beginning to impact biological research and biomedical applications as a result of its ability to integrate vast datasets, learn arbitrarily complex relationships and incorporate existing knowledge. Already, deep learning models can predict, with varying degrees of success, how genetic variation alters cellular processes involved in pathogenesis, which small molecules will modulate the activity of therapeutically relevant proteins, and whether radiographic images are indicative of disease. However, the flexibility of deep learning creates new challenges in guaranteeing the performance of deployed systems and in establishing trust with stakeholders, clinicians and regulators, who require a rationale for decision making. We argue that these challenges will be overcome using the same flexibility that created them; for example, by training deep models so that they can output a rationale for their predictions. Significant research in this direction will be needed to realize the full potential of deep learning in biomedicine.