Catalysts and processes designed to convert DME and/or methanol and hydrogen (H2) to desirable liquid fuels are described. These catalysts produce the fuels efficiently and with a high selectivity and yield, and reduce the formation of aromatic hydrocarbons by incorporating H2 into the products. Also described are process methods to further upgrade these fuels to higher molecular weight liquid fuel mixtures, which have physical properties comparable with current commercially used liquid fuels.