Many modern datasets possess complex correlation structures. Such data is typically stored as graphs. Examples of graph data include social networks, web graphs, biological networks, and neural networks. These graph datasets often contain hundreds of millions of nodes and billions of edges, which leads to a significant problem in terms of storage and processing. Therefore, there is need to compress graphs and store them efficiently without losing much information. In this talk, I will give an introduction to the developing field of graph compression. I will discuss the basic problems encountered in practice and some of the solutions that have been proposed. I will also present a few results detailing information theoretic limits on compressing graphs.