The image of dairy farming systems is increasingly being scrutinized by welfare organizations, activist groups and the public with intensive systems getting the most attention. So-called factory farms are being regarded by the public as not ideal for the production of products like milk and meat. Dairy cows, being ruminants, contribute directly to greenhouse gas emissions (GHG) because of the way feed is digested. By comparing past to present production systems, it has been demonstrated that the efficiency of milk production has increased over the last 40 years resulted in lower GHG emissions per kg of milk produced. The best way to reduce the impact of livestock production on climate change is to improve the efficiency of production systems. This can be done by (1) higher milk yields and improved fertility in heifers and cows, (2) improving feed quality and management by reducing feed shrinkage during forage harvesting, feed delivery and storage, mixing and delivery of feeds and (3) to breed for cows producing less methane in the production of milk. Genetic gain is, however, a function of the accuracy of selection and genetic variation. Large quantities of data are required to estimate reliable genetic parameters for methane production. As the accuracy of directly measuring methane production cows would be difficult, an indirect indicator or associated trait would be required. The genetic correlation between direct methane production and the indicator trait would give an indication of such a possibility. As the amount of methane produced by cows is correlated to milk yield levels it would be possible to decrease the methane production of cows by selecting more efficient cows. The genetic variation suggests that reductions in the order of 11 to 26% in 10 years are theoretically possible.