We explore the greenhouse-gas emission reductions necessary to achieve long-term global climate goals, such as holding warming below 1.5 and 2°C warming relative to pre-industrial levels. Analysing emissions scenarios from energy-economic models and other sources with coupled carbon-cycle/climate models leads to globally “allowed” ranges of emissions for different greenhouse gases, air pollutants and sectors, as well as associated time- and pathway-dependent mitigation costs and technology portfolios.