Ultra-compact binaries as gravitational wave sources

Ultra-compact binaries are among the most numerous sources in the millihertz gravitational wave band, and as such represent one of the primary sources for LISA-like detectors (gravitational wave interferometers in space). Already there are almost 60 ultra-compact binaries that have been detected by electromagnetic means, and more are being discovered in dedicated searches as time goes on. Prominent in this population is the doubly-degenerate white dwarf system J0651, whose orbital decay has been measured and shown to track accurately with the predicted evolution due to the emission of gravitational wave emission. This paper reviews the current understanding of the ultra-compact binary population, recent progress in electromagnetic studies, and prospects for multi-messenger astronomy of these systems once a LISA-like detector is operational. (paper)