We live in a highly interconnected world where many physical, social, biological, and technological systems consist of agents or entities interacting with each other. Examples include a virus being transmitted over social contact networks, global trade between countries, and the human brain. Any such system can be represented as a network by denoting the agents/entities as vertices and the interactions between them as edges. This makes networks an important and ubiquitous type of data spanning a remarkable variety of complex systems. It is therefore very important to have mathematically rigorous and practically useful methods for statistical analysis of networks. However, the structure and configuration of networks are quite different from that of traditional forms of statistical data, which means that new statistical methodology is needed for realistic modeling and reliable inference for network data. Fittingly, the last two decades have seen a remarkable surge in research aimed at developing statistical methodology for network data. This article provides a brief overview of this rapidly evolving field of statistics, which encompasses statistical models, algorithms, and inferential methods for analyzing data in the form of networks. Particular emphasis is given to connecting the historical developments in network science to today’s statistical network analysis and outlining important new areas for future research.