Theories of economic growth have long recognised that innovation is a key but poorly understood force – the 'residual' of neoclassical growth models. These models have no representation of intermediate goods, or of the factors that generate and diffuse innovations, including learning-by-doing and scale economies; they are thus unable to picture how a suite of economic and institutional changes triggers waves of long-term economic progress, which in practice has been the long-term historical pattern. The absence of finance in these models is particularly problematic. The centrality of financial structures to understanding patterns of economic growth is acute concerning policies to shape efficiency, innovation and infrastructure in ways compatible with energy and climate security, since these require substantial upfront investment. However, uncertainty and a lack of confidence deter such investment. Environmental policy could reduce risk and thereby shape ultimately profitable investments. The paper outlines deep relationships between energy/carbon-related finance and wider debates about financial systems after the crisis. The paper finally proposes an agenda for future