Galactic white dwarf binaries will be an abundant source of gravitational waves in the mHz frequency band of space-based detectors such as eLISA. A few thousand to a few tens of thousands of these systems will be individually resolvable by eLISA, depending on the final detector configuration. The remaining tens of millions of close white dwarf binaries will create an unresolvable anisotropic foreground of gravitational waves that will be comparable to the instrument noise of eLISA at frequencies below about a mHz. Both the resolvable binaries and the foreground can be used to better understand this population. Careful choice of the initial orientation of eLISA can mitigate this foreground in searches for other sources.
