We describe collaboration networks consisting of research projects funded by the European Union (EU) and the organizations involved in those projects. The networks are substantial in terms of size, complexity, and potential impact on research policies and national economies in the EU. In empirical determinations of the network properties, we observe characteristics similar to those of other collaboration networks, including scale-free degree distributions, small diameter, and high clustering. We present some plausible models for the formation and structure of networks with the observed properties.