Binary stars are crucial laboratories for stellar physics, so have been photometric targets for space missions beginning with the very first orbiting telescope (OAO-2) launched in 1968. This review traces the binary stars observed and the scientific results obtained from the early days of ultraviolet missions (OAO-2, Voyager, ANS, IUE), through a period of diversification (Hipparcos, WIRE, MOST, BRITE), to the current era of large planetary transit surveys (CoRoT, Kepler, TESS). In this time observations have been obtained of detached, semi-detached and contact binaries containing dwarfs, sub-giants, giants, supergiants, white dwarfs, planets, neutron stars and accretion discs. Recent missions have found a huge variety of objects such as pulsating stars in eclipsing binaries, multi-eclipsers, heartbeat stars and binaries hosting transiting planets. Particular attention is paid to eclipsing binaries, because they are staggeringly useful, and to the NASA Transiting Exoplanet Survey Satellite (TESS) because its huge sky coverage enables a wide range of scientific investigations with unprecedented ease. These results are placed into context, future missions are discussed, and a list of important science goals is presented.