Eclipsing binaries, both inside and outside our Galaxy, are proving to be powerful tools for studying a wide spectrum of astrophysical problems. They are also are extremely valuable for providing fundamental quantities such as stellar masses, radii, luminosities, ages and distances. Recently, eclipsing binaries are turning out to be accurate distance indicators for star clusters inside our Galaxy and for determining accurate distances to nearby galaxies – such as the Magellanic Clouds and the Andromeda Galaxy. Also with eclipsing binaries, it is possible to study the physical properties and determine evolution for a wide variety of objects that are lucky enough to be binary members. These objects include pre-main sequence stars, main sequence stars, giants, supergiants, various pulsating stars, white dwarfs, black holes and even exosolar planets. At the present time over 7000 eclipsing binaries have been discovered in Local Group galaxies. These systems are mostly members of the Magellanic Clouds and the Andromeda Galaxy. But also an increasing number of extragalactic binaries are being found as members of dwarf elliptical galaxies and low surface density irregular galaxy members of the Local Group. It will be important to study the properties of eclipsing binaries that have formed in galaxies with vastly different dynamical, star formation, and chemical histories than our home Galaxy. The study of these binaries may provide clues about the star formation rates and dynamics of their host galaxies as well as the possible effects of varying chemical abundance on stellar evolution and structure. An overview of eclipsing and interacting binary star systems in exterior galaxies is presented that traces the development of this emerging field of research. Also discussed are some recent developments and future expectations for the study of extragalactic binaries.