Analogy is core to human cognition. It allows us to solve problems based on prior experience, it governs the way we conceptualize new information, and it even influences our visual perception. The importance of analogy to humans has made it an active area of research in the broader field of artificial intelligence, resulting in data-efficient models that learn and reason in human-like ways. While analogy and deep learning have generally been considered independently of one another, the integration of the two lines of research seems like a promising step towards more robust and efficient learning techniques. As part of the first steps towards such an integration, we introduce the Analogical Matching Network; a neural architecture that learns to produce analogies between structured, symbolic representations that are largely consistent with the principles of Structure-Mapping Theory.