Understanding the causes and consequences of, and devising countermeasures to, global warming is a profoundly complex problem. Even when researchers narrow down the focus to a publishable investigation, their analysis often contains enough interacting components to require a network visualization. Networks are thus both necessary and natural elements of climate science. Furthermore, networks form a mathematical foundation for a multitude of computational and analytical techniques. We are only beginning to see the benefits of this connection between the sciences of climate change and networks. In this review, we cover use-cases of networks in the climate-change literature – what they represent, how they are analyzed, and what insights they bring. We also discuss network data, tools, and problems yet to be explored.