The atmospheric methane burden is increasing rapidly, contrary to pathways compatible with the goals of the 2015 United Nations Framework Convention on Climate Change Paris Agreement. Urgent action is required to bring methane back to a pathway more in line with the Paris goals. Emission reduction from “tractable” (easier to mitigate) anthropogenic sources such as the fossil fuel industries and landfills is being much facilitated by technical advances in the past decade, which have radically improved our ability to locate, identify, quantify, and reduce emissions. Measures to reduce emissions from “intractable” (harder to mitigate) anthropogenic sources such as agriculture and biomass burning have received less attention and are also becoming more feasible, including removal from elevated‐methane ambient air near to sources. The wider effort to use microbiological and dietary intervention to reduce emissions from cattle (and humans) is not addressed in detail in this essentially geophysical review. Though they cannot replace the need to reach “net‐zero” emissions of CO2, significant reductions in the methane burden will ease the timescales needed to reach required CO2 reduction targets for any particular future temperature limit. There is no single magic bullet, but implementation of a wide array of mitigation and emission reduction strategies could substantially cut the global methane burden, at a cost that is relatively low compared to the parallel and necessary measures to reduce CO2, and thereby reduce the atmospheric methane burden back toward pathways consistent with the goals of the Paris Agreement. Plain Language Summary Methane is a powerful climate warmer, and the amount of methane in the air is growing rapidly. Reducing human‐caused methane emissions is urgent if the 2015 United Nations Paris Agreement to limit climate warming is to succeed. There is hope, though the problem of methane mitigation is very wide and complex. Much of the task is in finding, identifying, and quantifying emissions. Rapid technical advances are making it much easier to locate and thus cut emissions from fossil fuel industries (gas, coal, and oil). Assessing emissions from landfill and sewage facilities is also becoming easier. In particular, poorly regulated landfills in fast‐growing tropical megacities need attention. Agricultural emissions are less tractable but may also be reduced to some extent, especially by improving manure management. Many methane mitigation options offer cost‐effective approaches to cut global warming and bring the amount of methane in the air back to a pathway that is consistent with the aims of the Paris Agreement. Key Points The atmospheric methane burden is rising fast; this growth is an increasing threat to the Paris Agreement of the UN Framework Convention on Climate Change (UNFCCC) New gas measurement technologies, on the ground and in the air, have greatly improved our ability to locate and quantify emissions and to identify mitigation targets Emissions can be cut by ending fossil fuel emissions, cutting biomass burning, improving landfills, especially in the tropics, and changing cattle farming practice