Summary. The existence of gravitational waves is the most prominent of Einstein's predictions that has not yet been directly verified. The space project LISA shares its goal and principle of operation with the ground-based interferometers currently being operated, the detection and measurement of gravitational waves by laser interferometry. Ground and space detection differ in their frequency ranges, and thus in the detectable sources. Toward low frequencies, ground-based detection is limited by seismic noise, and yet more fundamentally by "gravity-gradient noise," thus covering the range from a few Hz on upward to a few kHz. It is only in space that detection of signals below, say, 1 Hz is possible, opening a wide window to a different class of interesting sources of gravitational waves. The project LISA consists of three spacecraft in heliocentric orbits, forming a triangle of 5 million km sides. A technology demonstrator, the LISA Pathfinder, designed to test vital LISA technologies, is to be launched by ESA in 2009.LISA will face great challenges in reducing measurement noise, and thus, it will very strongly depend on the technologies of lasers, clocks, and drag-free control.