  Significant advances have been made in the understanding of the diffuse
Galactic hard X-ray continuum emission using data from the INTEGRAL
observatory. The diffuse hard power-law component seen with the INTEGRAL/SPI
spectrometer has been identified with inverse-Compton emission from
relativistic (GeV) electrons on the cosmic microwave background and Galactic
interstellar radiation field. In the present analysis, SPI data from 2003 to
2009, with a total exposure time of ~ 10^8 s, are used to derive the Galactic
ridge hard X-ray spatial distribution and spectrum between 20 keV and 2.4 MeV.
Both are consistent with predictions from the GALPROP code. The good agreement
between measured and predicted emission from keV to GeV energies suggests that
the correct production mechanisms have been identified. We discuss the
potential of the SPI data to provide an indirect probe of the interstellar
cosmic-ray electron distribution, in particular for energies below a few GeV.
