This essay analyzes critically the idea of knowledge spillovers, especially as it enters the New Growth Theory. The conventional theory of spillovers, we argue, suffers from a thin and misleading account of the nature of productive knowledge. In this model, firms undersupply R&D, which impedes economic growth and calls for research subsidies. We argue, by contrast, that a more subtle picture of the creation of knowledge, and the presence of network externalities (including true Marshallian external economies), tend to reverse the predictions of neoclassical theory: spillovers may actually lead to increases in the production of new knowledge.