This chapter introduces the concept of a memcapacitor, and reviews different approaches to its physical realization. Also, practical constraints for their usage are assessed. Because of their compatibility with traditional circuit integration technologies, two approaches are particularly interesting: the ferroelectric capacitor and the memcapacitor constructed by appending metal-insulator-metal (MIM) capacitor with a memristive switching layer. Ferroelectric capacitors have already been in use for many years so the properties of this technology are relatively well researched. The MIM-memristor hybrid structure can take advantage of the vital research on memristive memories. With sufficiently large ratio of the OFF and ON resistances of a memristive material, the compound structure behaves as a memcapacitive system. Finally, the potential of memcapacitors for memory and logic applications as well as for artificial neural networks are discussed.