With the observations of the ground-based and space γ -ray telescopes, the study on the origin of cosmic rays (CRs) has been deepened. As sources of CRs below the “knee” energy, the sample of supernova remnants (SNRs) with GeV-TeV γ -ray emission is being enlarged, getting to show some statistical properties in flux, spectra, etc. Appreciable observational and theoretical efforts have been made to investigate the radiation mechanisms of the γ -ray emission from SNRs and, especially, the hadronic interaction between SNRs and molecular clouds (MCs) so as to verify the scenario that relativistic protons, as the main component of CRs, can be produced by the SNR shocks. The detection of characteristic π0 -decay bump at 70 MeV in SNRs W44 and IC 443 marks a great progress in this regard. There are essentially two types of models explaining the hadronic γ -ray emission: direct proton-MC collision at the SNR shocks and MC “illumination” by escaped protons. A lot of work still need to do, such as systematic researches with a larger sample of γ -ray emitting SNRs, reasonable model calculation of the SNR emission in γ -rays together with other wavelengths, investigation of the molecular environment of SNRs, and even basic distinguishing of hardronic/leptonic property of the γ -ray emission. In this article, we will briefly summarize the present status of the above-mentioned studies.
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