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In this article, which will appear as a chapter in the Handbook of Gravitational Wave Astronomy, we will describe the detection of gravitational waves with space-based interferometric gravitational wave observatories. We will provide an overview of the key technologies underlying their operation, illustrated using the specific example of the Laser Interferometer Space Antenna (LISA). We will then give an overview of data analysis strategies for space-based detectors, including a description of time-delay interferometry, which is required to suppress laser frequency noise to the necessary level. We will describe the main sources of gravitational waves in the millihertz frequency range targeted by space-based detectors and then discuss some of the key science investigations that these observations will facilitate. Once again, quantitative statements given here will make reference to the capabilities of LISA, as that is the best studied mission concept. Finally, we will describe some of the proposals for even more sensitive space-based detectors that could be launched further in the future.