Despite the fact that deep learning has achieved remarkable success in various domains over the past decade, its application in molecular informatics and drug discovery is still limited. Recent advances in adapting deep architectures to structured data have opened a new paradigm for pharmaceutical research. In this survey, we provide a systematic review on the emerging field of graph convolutional networks and their applications in drug discovery and molecular informatics. Typically we are interested in why and how graph convolution networks can help in drug-related tasks. We elaborate the existing applications through four perspectives: molecular property and activity prediction, interaction prediction, synthesis prediction and de novo drug design. We briefly introduce the theoretical foundations behind graph convolutional networks and illustrate various architectures based on different formulations. Then we summarize the representative applications in drug-related problems. We also discuss the current challenges and future possibilities of applying graph convolutional networks to drug discovery.