Although livestock production accounts for a sizeable share of global greenhouse gas emissions, numerous technical options have been identified to mitigate these emissions. In this review, a subset of these options, which have proven to be effective, are discussed. These include measures to reduce CH4 emissions from enteric fermentation by ruminants, the largest single emission source from the global livestock sector, and for reducing CH4 and N2O emissions from manure. A unique feature of this review is the high level of attention given to interactions between mitigation options and productivity. Among the feed supplement options for lowering enteric emissions, dietary lipids, nitrates and ionophores are identified as the most effective. Forage quality, feed processing and precision feeding have the best prospects among the various available feed and feed management measures. With regard to manure, dietary measures that reduce the amount of N excreted (e.g. better matching of dietary protein to animal needs), shift N excretion from urine to faeces (e.g. tannin inclusion at low levels) and reduce the amount of fermentable organic matter excreted are recommended. Among the many 'end-of-pipe' measures available for manure management, approaches that capture and/or process CH4 emissions during storage (e.g. anaerobic digestion, biofiltration, composting), as well as subsurface injection of manure, are among the most encouraging options flagged in this section of the review. The importance of a multiple gas perspective is critical when assessing mitigation potentials, because most of the options reviewed show strong interactions among sources of greenhouse gas (GHG) emissions. The paper reviews current knowledge on potential pollution swapping, whereby the reduction of one GHG or emission source leads to unintended increases in another.