The purpose of this investigation is to understand and improve palladium membrane oxidative pumping for large quantities of hydrogen gas at vacuum pressures. Oxidative pumping should be exceptionally fast, clean, and energy efficient. Hydrogen molecules are chemisorbed and dissociated on one surface of a palladium or palladium-coated membrane. Dissociated hydrogen atoms diffuse through the membrane and react with oxygen on the other side. Product water is removed by condensation at low temperatures. In this paper we analyze theory and relevant experiments concerning surface and bulk effects in hydrogen pumping with palladium membranes. Models are refined by comparison with experimental pumping data to suggest that the original pump design was limited by a low effective sticking coefficient, which apparently was caused by multiple pathways for dissociation on the palladium surface. Increased pumping speeds and increased economy should result from decreased operating temperatures, with 300 °C appearing as something of an optimum. At very low temperatures, surface oxidation, surface impedence, and low permeabilities will limit throughput. Commercial application appears limited to fusion reactors and to proton beam experiments.