We review recent progress in elucidating the relationship between high-energy radiation and the interstellar medium (ISM) in young supernova remnants (SNRs) with ages of $sim$2000 yr, focusing in particular on RX J1713.7$-$3946 and RCW 86. Both SNRs emit strong nonthermal X-rays and TeV $gamma$-rays, and they contain clumpy distributions of interstellar gas that includes both atomic and molecular hydrogen. We find that shock-cloud interactions provide a viable explanation for the spatial correlation between the X-rays and ISM. In these interactions, the supernova shocks hit the typically pc-scale dense cores, generating a highly turbulent velocity field that amplifies the magnetic field up to 0.1-1 mG. This amplification leads to enhanced nonthermal synchrotron emission around the clumps, whereas the cosmic-ray electrons do not penetrate the clumps. Accordingly, the nonthermal X-rays exhibit a spatial distribution similar to that of the ISM on the pc scale, while they are anticorrelated at sub-pc scales. These results predict that hadronic $gamma$-rays can be emitted from the dense cores, resulting in a spatial correspondence between the $gamma$-rays and the ISM. The current pc-scale resolution of $gamma$-ray observations is too low to resolve this correspondence. Future $gamma$-ray observations with the Cherenkov Telescope Array will be able to resolve the sub-pc-scale $gamma$-ray distribution and provide clues to the origin of these cosmic $gamma$-rays.
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