In Australia, agriculture is responsible for ~17% of total greenhouse gas emissions with ruminants being the largest single source. However, agriculture is likely to be shielded from the full impact of any future price on carbon. In this review, strategies for reducing ruminant methane output are considered in relation to rumen ecology and biochemistry, animal breeding and management options at an animal, farm, or national level. Nutritional management strategies have the greatest short-term impact. Methanogenic microorganisms remove H₂ produced during fermentation of organic matter in the rumen and hind gut. Cost-effective ways to change the microbial ecology to reduce H₂ production, to re-partition H₂ into products other than methane, or to promote methanotrophic microbes with the ability to oxidise methane still need to be found. Methods of inhibiting methanogens include: use of antibiotics; promoting viruses/bacteriophages; use of feed additives such as fats and oils, or nitrate salts, or dicarboxylic acids; defaunation; and vaccination against methanogens. Methods of enhancing alternative H₂ using microbial species include: inoculating with acetogenic species; feeding highly digestible feed components favouring 'propionate fermentations'; and modifying rumen conditions. Conditions that sustain acetogen populations in kangaroos and termites, for example, are poorly understood but might be extended to ruminants. Mitigation strategies are not in common use in extensive grazing systems but dietary management or use of growth promotants can reduce methane output per unit of product. New, natural compounds that reduce rumen methane output may yet be found. Smaller but more permanent benefits are possible using genetic approaches. The indirect selection criterion, residual feed intake, when measured on ad libitum grain diets, has limited relevance for grazing cattle. There are few published estimates of genetic parameters for feed intake and methane production. Methane-related single nucleotide polymorphisms have yet to be used commercially. As a breeding objective, the use of methane/kg product rather than methane/head is recommended. Indirect selection via feed intake may be more cost-effective than via direct measurement of methane emissions. Life cycle analyses indicate that intensification is likely to reduce total greenhouse gas output but emissions and sequestration from vegetation and soil need to be addressed. Bio-economic modelling suggests most mitigation options are currently not cost-effective.