In recent years, methods from network science have been rapidly gaining traction in economics and finance. One reason for this is that, in a globalized world, it is crucial that we understand the interconnections between economic and financial entities; networks provide a natural framework for representing and studying such systems. In this paper, we survey the use of networks and network-based methods to study economy-related questions. We start with a brief overview of graph theory and some basic definitions. Then, we discuss descriptive network measures and network complexity measures for quantifying the structural properties of economic networks. Finally, we discuss different network and tree structures as well as their relevance to certain applications.