Aspects of the invention are associated with the discovery of processes for converting methane (CH4), present in a methane-containing feedstock that may be obtained from a variety of sources such as natural gas, to higher hydrocarbons (e.g., C4+ hydrocarbons) such as gasoline, diesel fuel, or jet fuel boiling-range hydrocarbons, which may optionally be separated (e.g., by fractionation) for use as transportation fuels, or otherwise as blending components for such fuels. Particular aspects of the invention are associated with advantages arising from maintaining reaction conditions that improve the yield of C4+ hydrocarbons. Further aspects relate to the advantages gained by integration of the appropriate reactions to carry out the methane conversion, with downstream separation to recover and recycle desirable components of the reaction effluent, thereby improving process economics to the extent needed for commercial viability.