  Most of the celestial gamma rays detected by the Large Area Telescope (LAT)
aboard the Fermi Gamma-ray Space Telescope originate from the interstellar
medium when energetic cosmic rays interact with interstellar nucleons and
photons. Conventional point and extended source studies rely on the modeling of
this diffuse emission for accurate characterization. We describe here the
development of the Galactic Interstellar Emission Model (GIEM) that is the
standard adopted by the LAT Collaboration and is publicly available. The model
is based on a linear combination of maps for interstellar gas column density in
Galactocentric annuli and for the inverse Compton emission produced in the
Galaxy. We also include in the GIEM large-scale structures like Loop I and the
Fermi bubbles. The measured gas emissivity spectra confirm that the cosmic-ray
proton density decreases with Galactocentric distance beyond 5 kpc from the
Galactic Center. The measurements also suggest a softening of the proton
spectrum with Galactocentric distance. We observe that the Fermi bubbles have
boundaries with a shape similar to a catenary at latitudes below 20 degrees and
we observe an enhanced emission toward their base extending in the North and
South Galactic direction and located within 4 degrees of the Galactic Center.
