Abstract There have been several reports of methane on Mars at the 10–60 ppbv level. Most suggest that methane is both seasonally and latitudinally variable. Here we review why variable methane on Mars is physically and chemically implausible, and then we critically review the published reports. There is no known mechanism for destroying methane chemically on Mars. But if there is one, methane oxidation would deplete the O 2 in Mars’s atmosphere in less than 10,000 years unless balanced by an equally large unknown source of oxidizing power. Physical sequestration does not raise these questions, but adsorption in the regolith or condensation in clathrates ignore competition for adsorption sites or are inconsistent with clathrate stability, respectively. Furthermore, any mechanism that relies on methane’s van der Waals’ attraction is inconsistent with the continued presence of Xe in the atmosphere at the 60 ppbv level. We then use the HITRAN database and transmission calculations to identify and characterize the absorption lines that would be present on Earth or Mars at the wavelengths of the published observations. These reveal strong competing telluric absorption that is most problematic at just those wavelengths where methane’s signature seems most clearly seen from Earth. The competing telluric lines must be removed with models. The best case for martian methane was made for the 12 CH 4 ν 3 R0 and R1 lines seen in blueshift when Mars was approaching Earth in early 2003 (Mumma, M.J., Villanueva, G.L., Novak, R.E., Hewagama, T., Bonev, B.P., DiSanti, M.A., Mandell, A.M., Smith, M.D. [2009]. Science 323, 1041–1045). For these the Doppler shift moves the two martian lines into near coincidence with telluric 13 CH 4 ν 3 R1 and R2 lines that are 10–50× stronger than the inferred martian lines. By contrast, the 12 CH 4 ν 3 R0 and R1 lines when observed in redshift do not contend with telluric 13 CH 4 . For these lines, Mumma et al.’s observations and analyses are consistent with an upper limit on the order of 3 ppbv.