Deep learning describes a class of machine learning algorithms that are capable of combining raw inputs into layers of intermediate features. These algorithms have recently shown impressive results across a variety of domains. Biology and medicine are data-rich disciplines, but the data are complex and often ill-understood. Hence, deep learning techniques may be particularly well suited to solve problems of these fields. We examine applications of deep learning to a variety of biomedical problems-patient classification, fundamental biological processes and treatment of patients-and discuss whether deep learning will be able to transform these tasks or if the biomedical sphere poses unique challenges. Following from an extensive literature review, we find that deep learning has yet to revolutionize biomedicine or definitively resolve any of the most pressing challenges in the field, but promising advances have been made on the prior state of the art. Even though improvements over previous baselines have been modest in general, the recent progress indicates that deep learning methods will provide valuable means for speeding up or aiding human investigation. Though progress has been made linking a specific neural network's prediction to input features, understanding how users should interpret these models to make testable hypotheses about the system under study remains an open challenge. Furthermore, the limited amount of labelled data for training presents problems in some domains, as do legal and privacy constraints on work with sensitive health records. Nonetheless, we foresee deep learning enabling changes at both bench and bedside with the potential to transform several areas of biology and medicine.