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Diffusive shock acceleration at the outer front of expanding supernova remnants has provided by far the most popular model for the origin of galactic cosmic rays, and has been the subject of intensive theoretical investigation. But several problems loomed at high energies—how to explain the smooth continuation of the cosmic-ray spectrum far beyond 1014 eV, the very low level of TeV gamma-ray emission from several supernova remnants, and the very low anisotropy of cosmic rays (seeming to conflict with the short trapping times needed to convert a E-2 source spectrum into the observed E-2.7 spectrum of cosmic rays). However, recent work on the cosmic ray spectrum (especially at KASCADE) strongly indicates that about half of the flux does turn down rather sharply near 3 × 1015 V rigidity, with a distinct tail extending to just beyond 1017 V rigidity; whilst a plausible description (Bell and Lucek) of the level of self-generated magnetic fields at the shock fronts of young supernova remnants implies that many SNRs in varying environments might very well generate spectra extending smoothly to just this 'knee' position, and a portion of the exploding red supergiants could extend the spectrum approximately as needed. At low energies, recent progress in relating cosmic ray compositional details to modified shock structure also adds weight to the belief that the model is working on the right lines, converting energy into cosmic rays very efficiently where injection can occur. The low level of TeV gamma-ray flux from many young SNRs is a serious challenge, though it may relate to variations in particle injection efficiency with time. The clear detection of TeV gamma rays from SNRs has now just begun, and predictions of a characteristic curved particle spectrum give a target for new tests by TeV observations. However, the isotropy seriously challenges the assumed cosmic-ray trapping time and hence the shape of the spectrum of particles released from SNRs. There is otherwise enough convergence of model and observation to encourage belief that the outline of the model is right, but there remains the possibility that the spectral shape of particles actually released is not as previously predicted.