  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.
