We summarize some recent results related to observations and interpret
ation of hard X-ray and low-energy gamma-ray diffuse Galactic continuu
m emission. Combined spectra based on data from OSSE, COMPTEL and EGRE
T are presented. In the energy range 1-30 MeV covered by COMPTEL the s
pectrum of the diffuse emission has been measured and is consistent wi
th a combination of bremsstrahlung and inverse-Compton emission; spati
al analysis shows strong evidence for a component with a wide latitude
extent which is plausibly identified with inverse-Compton. Molecular
hydrogen appears to be only a weak gamma-ray emitter at low energies,
which may indicate reduced MeV cosmic-ray electron density in molecula
r clouds. New data on the hard X-ray diffuse Galactic emission from OS
SE indicates the need for a dramatic low-energy upturn in the electron
spectrum, or for some other additional component of gamma-ray emissio
n. The interstellar electron spectrum has been computed using a diffus
ive halo model and the resulting bremsstrahlung and inverse-Compton em
ission is compared with the observations.