Neuroscience research is undergoing a minor revolution. Recent advances in machine learning and artificial intelligence research have opened up new ways of thinking about neural computation. Many researchers are excited by the possibility that deep neural networks may offer theories of perception, cognition and action for biological brains. This approach has the potential to radically reshape our approach to understanding neural systems, because the computations performed by deep networks are learned from experience, and not endowed by the researcher. If so, how can neuroscientists use deep networks to model and understand biological brains? What is the outlook for neuroscientists who seek to characterize computations or neural codes, or who wish to understand perception, attention, memory and executive functions? In this Perspective, our goal is to offer a road map for systems neuroscience research in the age of deep learning. We discuss the conceptual and methodological challenges of comparing behaviour, learning dynamics and neural representations in artificial and biological systems, and we highlight new research questions that have emerged for neuroscience as a direct consequence of recent advances in machine learning.