Recent development of the gamma-ray astronomy is remarkable in both
on-board and the ground-based observations, for instance FERMI and
HESS respectively. I concentrate my talk upon the diffuse emission
induced by the interactions between CRs and interstellar gas (ISM),
mostly with hydrogen, and the interstellar radiation field (ISRF) with
(virtual) photon gas. I first touch brefly upon the elementary
processes to produce gamma-rays in these interactions, namely ~~~in
proton-ISM, bremsstrahlung in electron-ISM, inverse Compton in
electron-photon, and synchrotron in electron-magetic field, and then
compare the diffusion-halo model with the observational data including
most recent ones from FERMI.