Gravitational waves of low frequencies (below 1 Hz) cannot be measured by terrestrial detectors, due to many noise contributions in that frequency range. Laser interferometers in space, with huge arm-lengths, have been proposed and are under active study. The most prominent of these, LISA, has been studied in a NASA/ESA collaboration.Its arm-lengths of 5 million km will allow measuring GWs from cosmological events stemming from distant galaxies and involving massive black holes. The envisaged sensitivities would allow a deep insight into many cosmological questions. Plans are under way in China to take an active part in realizing a space detector beyond the specifications of LISA. The launch of a technology demonstrator mission, the LISA Pathfinder, is within a few years from now. It will verify the key technologies that are crucial for LISA, but also for other space missions using laser interferometry.