Measuring and mitigating methane (CH4) emissions from livestock is of increasing importance for the environment and for policy making. Potentially, the most sustainable way of reducing enteric CH4 emission from ruminants is through the estimation of genomic breeding values to facilitate genetic selection. There is potential for adopting genetic selection and in the future genomic selection, for reduced CH4 emissions from ruminants. From this review it has been observed that both CH4 emissions and production (g/day) are a heritable and repeatable trait. CH4 emissions are strongly related to feed intake both in the short term (minutes to several hours) and over the medium term (days). When measured over the medium term, CH4 yield (MY, g CH4/kg dry matter intake) is a heritable and repeatable trait albeit with less genetic variation than for CH4 emissions. CH4 emissions of individual animals are moderately repeatable across diets, and across feeding levels, when measured in respiration chambers. Repeatability is lower when short term measurements are used, possibly due to variation in time and amount of feed ingested prior to the measurement. However, while repeated measurements add value; it is preferable the measures be separated by at least 3 to 14 days. This temporal separation of measurements needs to be investigated further. Given the above issue can be resolved, short term (over minutes to hours) measurements of CH4 emissions show promise, especially on systems where animals are fed ad libitum and frequency of meals is high. However, we believe that for short-term measurements to be useful for genetic evaluation, a number (between 3 and 20) of measurements will be required over an extended period of time (weeks to months). There are opportunities for using short-term measurements in standardised feeding situations such as breath 'sniffers' attached to milking parlours or total mixed ration feeding bins, to measure CH4. Genomic selection has the potential to reduce both CH4 emissions and MY, but measurements on thousands of individuals will be required. This includes the need for combined resources across countries in an international effort, emphasising the need to acknowledge the impact of animal and production systems on measurement of the CH4 trait during design of experiments.