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Anthropogenic methane (CH4) emissions increases from the period 1850–1900 until 2019 are responsible for around 65% as much warming as carbon dioxide (CO2) has caused to date, and large reductions in methane emissions are required to limit global warming to 1.5°C or 2°C. However, methane emissions have been increasing rapidly since ~2006. This study shows that emissions are expected to continue to increase over the remainder of the 2020s if no greater action is taken and that increases in atmospheric methane are thus far outpacing projected growth rates. This increase has important implications for reaching net zero CO2 targets: every 50 Mt CH4 of the sustained large cuts envisioned under low-warming scenarios that are not realized would eliminate about 150 Gt of the remaining CO2 budget. Targeted methane reductions are therefore a critical component alongside decarbonization to minimize global warming. We describe additional linkages between methane mitigation options and CO2, especially via land use, as well as their respective climate impacts and associated metrics. We explain why a net zero target specifically for methane is neither necessary nor plausible. Analyses show where reductions are most feasible at the national and sectoral levels given limited resources, for example, to meet the Global Methane Pledge target, but they also reveal large uncertainties. Despite these uncertainties, many mitigation costs are clearly low relative to real-world financial instruments and very low compared with methane damage estimates, but legally binding regulations and methane pricing are needed to meet climate goals.