The evidence for particle acceleration in supernova shells comes from electrons whose synchrotron emission is observed in radio and X-rays. Recent observations by the HESS instrument reveal that supernova remnants also emit TeV {gamma}-rays; long awaited experimental evidence that supernova remnants can accelerate cosmic rays up to the ''knee'' energies. Still, uncertainty exists whether these {gamma}-rays are produced by electrons via inverse Compton scattering or by protons via {pi}{sup 0}-decay. The multi-wavelength spectra of supernova remnants can be fitted with both mechanisms, although a preference is often given to {pi}{sup 0}-decay due to the spectral shape at very high energies. A recent study of the interstellar radiation field i...