Biomedical networks are universal descriptors of systems of interacting elements, from protein interactions to disease networks, all the way to healthcare systems and scientific knowledge. With the remarkable success of representation learning in providing powerful predictions and insights, we have witnessed a rapid expansion of representation learning techniques into modeling, analyzing, and learning with such networks. In this review, we put forward an observation that long-standing

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... of networks in biology and medicine -- while often unspoken in machine learning research -- can provide the conceptual grounding for representation learning, explain its current successes and limitations, and inform future advances. We synthesize a spectrum of algorithmic approaches that, at their core, leverage graph topology to embed networks into compact vector spaces, and capture the breadth of ways in which representation learning is proving useful. Areas of profound impact include identifying variants underlying complex traits, disentangling behaviors of single cells and their effects on health, assisting in diagnosis and treatment of patients, and developing safe and effective medicines.