The IPCC warns that in order to keep global warming under 1.5 degrees, global emissions must be cut to zero by 2050. Policymakers and scholars debate how best to decarbonise the energy system, and what socio-economic changes might be necessary. Here we review the strengths, weaknesses, and synergies of two prominent climate change mitigation narratives: the Green New Deal and degrowth. Green New Deal advocates propose a plan to coordinate and finance a large-scale overhaul of the energy system. Some see economic growth as crucial to financing this transition, and claim that the Green New Deal will further stimulate growth. By contrast, proponents of degrowth maintain that growth makes it more difficult to accomplish emissions reductions, and argue for reducing the scale of energy use to enable a rapid energy transition. The two narratives converge on the importance of public investments for financing the energy transition, industrial policies to lead the decarbonisation of the economy, socializing the energy sector to allow longer investment horizons, and expanding the welfare state to increase social protection. We conclude that despite important tensions, there is room for synthesizing Green New Deal and degrowth-minded approaches into a 'Green New Deal without growth'.