The millions of reactions performed and compounds synthesized by organic chemists over the past two centuries connect to form a network larger than the metabolic networks of higher organisms and rivalling the complexity of the World Wide Web. Despite its apparent randomness, the network of chemistry has a well-defined, modular architecture. The network evolves in time according to trends that have not changed since the inception of the discipline, and thus project into chemistry's future. Analysis of organic chemistry using the tools of network theory enables the identification of most 'central' organic molecules, and for the prediction of which and how many molecules will be made in the future. Statistical analyses based on network connectivity are useful in optimizing parallel syntheses, in estimating chemical reactivity, and more.