  Double white dwarf (DWD) binaries are expected to be very common in the Milky
Way, but their intrinsic faintness challenges the detection of these systems.
Currently, only a few tens of detached DWDs are know. Such systems offer the
best chance of extracting the physical properties that would allow us to
address a wealth of outstanding questions ranging from the nature of white
dwarfs, over stellar and binary evolution to mapping the Galaxy. In this paper
we explore the prospects for detections of ultra-compact (with binary
separations of a few solar radii or less) detached DWDs in: 1) optical
radiation with Gaia and the LSST and 2) gravitational wave radiation with LISA.
We show that Gaia, LSST and LISA have the potential to detect respectively
around a few hundreds, a thousand, and 25 thousand DWD systems. Moreover, Gaia
and LSST data will extend by respectively a factor of two and seven the
guaranteed sample of binaries detected in electromagnetic and gravitational
wave radiation, opening the era of multi-messenger astronomy for these sources.
