Lithium-air (Li-air) batteries have a much higher theoretical energy density than conventional lithium batteries and other metal air batteries, so they are being developed for applications that require long life. Water vapor from air must be prevented from corroding the lithium (Li) metal negative electrode during discharge under ambient conditions, i.e., in humid air. One method of protecting the Li metal from corrosion is to use an oxygen selective membrane (OSM) that allows oxygen into the cell while stopping or slowing the ingress of water vapor. The desired properties and some potential materials for OSMs for Li-air batteries are discussed and the literature is reviewed.