Livestock production is a major contributor to greenhouse gas (GHG) emissions, so will play a significant role in the mitigation effort. Recent literature highlights different strategies to mitigate GHG emissions in the livestock sector. Animal welfare is a criterion of sustainability and any strategy designed to reduce the carbon footprint of livestock production should consider animal welfare amongst other sustainability metrics. We discuss and tabulate the likely relationships and trade-offs between the GHG mitigation potential of mitigation strategies and their welfare consequences, focusing on ruminant species and on cattle in particular. The major livestock GHG mitigation strategies were classified according to their mitigation approach as reducing total emissions (inhibiting methane production in the rumen), or reducing emissions intensity (Ei; reducing CH4 per output unit without directly targeting methanogenesis). Strategies classified as antimethanogenic included chemical inhibitors, electron acceptors (i.e. nitrates), ionophores (i.e. Monensin) and dietary lipids. Increasing diet digestibility, intensive housing, improving health and welfare, increasing reproductive efficiency and breeding for higher productivity were categorized as strategies that reduce Ei. Strategies that increase productivity are very promising ways to reduce the livestock carbon footprint, though in intensive systems this is likely to be achieved at the cost of welfare. Other strategies can effectively reduce GHG emissions whilst simultaneously improving animal welfare (e.g. feed supplementation or improving health). These win-win strategies should be strongly supported as they address both environmental and ethical sustainability. In order to identify the most cost-effective measures for improving environmental sustainability of livestock production, the consequences of current and future strategies for animal welfare must be scrutinized and contrasted against their effectiveness in mitigating climate change.