Double white dwarfs and LISA

Close pairs of white dwarfs are potential progenitors of Type~Ia supernovae and they are common, with of order 100 -- 300 million in the Galaxy. As such they will be significant, probably dominant, sources of the gravitational waves detectable by LISA. In the context of LISA's goals for fundamental physics, double white dwarfs are a source of noise, but from an astrophysical perspective, they are of considerable interest in their own right. In this paper I discuss our current knowledge of double white dwarfs and their close relatives (and possible descendants) the AM~CVn stars. LISA will add to our knowledge of these systems by providing the following unique constraints: (i) an almost direct measurement of the Galactic merger rate of DWDs from the detection of short period systems and their period evolution, (ii) an accurate and precise normalisation of binary evolution models at the shortest periods, (iii) a determination of the evolutionary pathways to the formation of AM~CVn stars, (iv) measurements of the influence of tidal coupling in white dwarfs and its significance for stabilising mass transfer, and (v) discovery of numerous examples of eclipsing white dwarfs with the potential for optical follow-up to test models of white dwarfs.