This paper argues that cross-technology knowledge spillovers are critical for understanding policy's role in the transition to clean technology. I develop an endogenous growth model with clean and dirty technologies and a network of cross-technology spillovers. I derive formulas for the size and speed of technological transition, following a policy reform, which show that greater spillovers across technologies induce a faster transition but at the expense of a smaller long-run impact of policy. Such spillovers also prevent the lock-in of dirty technology. The economy's spillover structure can be summarized by a sufficient statistic matrix, which I estimate using patent citation data. Applying my model to US transportation and electricity generation, I find that cross-technology spillovers are mid-sized: they prevent lock-in but imply a slow transition with a high long-run impact of policy. I conclude by examining how cross-technology spillovers affect optimal clean innovation subsidies, deriving an innovation subsidy formula that holds for arbitrary carbon prices. Quantitatively, I find that optimal clean innovation subsidies are small, reflecting the low centrality of clean technologies in the spillover network. Hence, a "big push" of temporary clean innovation subsidies is not warranted.