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. The resulting formulas for the size and speed of technological transition, following a policy reform, show that greater spillovers induce faster transitions but reduce the long-run impact of policy. Such spillovers also prevent lock-in of dirty technology. Using patent citation data, I apply my model to US transportation and electricity generation and find that spillovers are mid-sized: they prevent lock-in but imply slow transitions with high long-run impact of policy. I then examine how cross-technology spillovers affect optimal policy, deriving innovation subsidy formulas under arbitrary carbon prices. Quantitatively, a "big push" of clean innovation subsidies is no longer optimal because the spillover network allows us to build toward clean technology in the future by innovating in other technologies today.