Ceramic membranes can be divided into dense and porous membranes. The materials, microstructure, and manufacturing methods are described and insights into current research topics are given. By adapting the material properties and tailoring microstructures, membranes and components suitable for a variety of processes can be developed. In applications, a distinction can be made between pure gas separation and membrane reactors. In the latter ones, in addition to gas separation, a chemical reaction takes place on one or both sides of the membrane. Membrane reactors can be used to produce basic chemicals or synthetic fuels. The supply of gases can be of interest for power plants, cement, steel or glassworks as well as for the medical sector or for mobile applications.