The diffuse gamma-ray continuum emission, which arises from cosmic-ray protons and electrons interacting with the interstellar matter and low energy photons, is the dominant feature of the gamma-ray sky. This emission has been studied from 0.05 MeV to over 50 GeV using the observations from OSSE, COMPTEL, and EGRET on the Compton Gamma-Ray Observatory. The OSSE observations show the diffuse continuum to be a composite of three independent components: e(+)e(-) anihilation line plus continuum, a soft low-energy component, and a dominant, hard component. The COMPTEL re suits are the first measurement of the diffuse emission at intermediate energies and the EGRET results have provided a much clearer image of the spatial and spectral distribution of this emission at higher energies. Although significant contributions from unresolved distributions of point sources cannot be excluded, particularly from the COMPTEL and OSSE data, the spectra. from the three instruments, from I MeV to about 1 GeV, can be explained with the sum of bremsstrahlung, nucleon-nucleon (pi(0) decay), and inverse Compton components. However, above about 1 GeV, the EGRET spectrum is harder than expected from the nucleon-nucleon spectrum derived from an E-p(-2.7) cosmic-ray proton spectrum observed in the Solar neighborhood. These observations and results are discussed in terms of the correctness of our interpretations of the observations, what does and what does not conform to the standard picture, the significance of these observations for cosmic-ray physics, and how much of the observed flux is due to point sources.