The present invention discloses microporous aluminophosphate (AlPO4) molecular sieve membranes and methods for making and using the same. The microporous AlPO4 molecular sieve membranes, particularly small pore microporous AlPO-14 and AlPO-18 molecular sieve membranes, are prepared by three different methods, including in-situ crystallization of a layer of AlPO4 molecular sieve crystals on a porous membrane support, coating a layer of polymer-bound AlPO4 molecular sieve crystals on a porous membrane support, and a seeding method by in-situ crystallization of a continuous second layer of AlPO4 molecular sieve crystals on a seed layer of AlPO4 molecular sieve crystals supported on a porous membrane support. The microporous AlPO4 molecular sieve membranes have superior thermal and chemical stability, good erosion resistance, high CO2 plasticization resistance, and significantly improved selectivity over polymer membranes for gas and liquid separations, including carbon dioxide/methane (CO2/CH4), carbon dioxide/nitrogen (CO2/N2), and hydrogen/methane (H2/CH4) separations.