Machine learning, especially neural network methods, is increasingly important in network analysis. This chapter will discuss the theoretical aspects of network embedding methods and graph neural networks. As we have seen, much of the success of advanced machine learning is thanks to useful representations—embeddings—of data. Embedding and machine learning are closely aligned. Translating network elements to embedding vectors and sending those vectors as features to a predictive model often leads to a simpler, more performant model than trying to work directly with the network. Embeddings help with network learning tasks, from node classification to link prediction. We can even embed entire networks and then use models to summarize and compare networks. But not only does machine learning benefit from embeddings, but embeddings benefit from machine learning. Inspired by the incredible recent progress with natural language data, embeddings created by predictive models are becoming more useful and important. Often these embeddings are produced by neural networks of various flavors, and we explore current approaches for using neural networks on network data.