Methane (CH4) is an important greenhouse gas, second only to CO2, and is emitted into the atmosphere at different concentrations from a variety of sources. However, unlike CO2, which has a quadrupole moment and can be captured both physically and chemically in a variety of solvents and porous solids, methane is completely non-polar and interacts very weakly with most materials. Thus, methane capture poses a challenge that can only be addressed through extensive material screening and ingenious molecular-level designs. Here we report systematic in silico studies on the methane capture effectiveness of two different materials systems, that is, liquid solvents (including ionic liquids) and nanoporous zeolites. Although none of the liquid solvents appears effective as methane sorbents, systematic screening of over 87,000 zeolite structures led to the discovery of a handful of candidates that have sufficient methane sorption capacity as well as appropriate CH4/CO2 and/or CH4/N-2 selectivity to be technologically promising.