This paper reviews the mainstream, resource economics, and ecological economics models of growth. A possible synthesis of energy-based and mainstream models is presented. This shows that when energy is scarce it imposes a strong constraint on the growth of the economy; however, when energy is abundant, its effect on economic growth is much reduced. The industrial revolution released the constraints on economic growth by the development of new methods of using coal and the discovery of new fossil fuel resources. Time-series analysis shows that energy and GDP cointegrate, and energy use Granger causes GDP when capital and other production inputs are included in the vector autoregression model. However, various mechanisms can weaken the links between energy and growth. Energy used per unit of economic output has declined in developed and some developing countries, owing to both technological change and a shift from poorer quality fuels, such as coal, to the use of higher quality fuels, especially electricity. Substitution of other inputs for energy and sectoral shifts in economic activity play smaller roles.