Supernova remnants (SNRs) are prime candidates for acceleration sites of cosmic rays. In the last ~15 years, X-ray and TeV gamma-ray observations of SNRs indeed provided evidence that expanding SNR shells are able to accelerate charged particles up to TeV energies. Improved sensitivities of X-ray and TeV gamma-ray instruments enabled not only the detection of nonthermal radiation but also detailed spectral and morphological studies of SNRs. A new window for those studies has recently been opened by the Large Area Telescope (LAT) aboard the Fermi Gamma-ray Space Telescope, which is sensitive to gamma rays in the GeV band. Fermi LAT data put new constraints on emission mechanisms of young SNRs such as RX J1713.7-3946, and RX J0852.0-4622, which are known also as emitters of non-thermal X-rays and TeV gamma rays. Another important finding by the Fermi LAT is bright GeV emission from middle-aged SNRs interacting with molecular clouds, such as W44, W51C, and IC 443. We summarize recent X-ray and gamma-ray observations of non-thermal emission from SNRs. We also discuss possible scenarios to explain multi-wavelength spectra of SNRs.

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