Graph Convolutional Networks (GCNs) have emerged as a promising approach to machine learning on Electronic Health Records (EHRs). By constructing a graph representation of patient data and performing convolutions on neighborhoods of nodes, GCNs can capture complex relationships and extract meaningful insights to support medical decision making. This survey provides an overview of the current research in applying GCNs to EHR data. We identify the key medical domains and prediction tasks where these models are being utilized, common benchmark datasets, and architectural patterns to provide a comprehensive survey of this field. While this is a nascent area of research, GCNs demonstrate strong potential to leverage the complex information hidden in EHRs. Challenges and opportunities for future work are also discussed.