ESA's second space astrometry mission Gaia started its scientific operations in July 2014. During its routine science operation Gaia is delivering an immense dataset of high-accuracy positional observations which already led to two Data Releases containing high-accuracy position, parallaxes and proper motions of over a billion sources. In this presentation we will briefly overview the principles and ideas of space astrometry with Gaia and emphasise that high-accuracy astrometry can be used as a gravitational wave detector. We will discuss details of this use of astrometry. We will argue that global astrometry of Gaia is most sensitive to continuous gravitational waves with frequencies below about 0.1 mHz. Binary super-massive black holes are typical sources that can produce such gravitational waves.