The origin of cosmic rays holds still many mysteries hundred years after they were first discovered. Supernova remnants have for long been the most likely sources of Galactic cosmic rays. I discuss here some recent evidence that suggests that supernova remnants can indeed efficiently accelerate cosmic rays. For this conference devoted to the Astronomical Institute Utrecht I put the emphasis on work that was done in my group, but placed in a broader context: efficient cosmic-ray acceleration and the im- plications for cosmic-ray escape, synchrotron radiation and the evidence for magnetic- field amplification, potential X-ray synchrotron emission from cosmic-ray precursors, and I conclude with the implications of cosmic-ray escape for a Type Ia remnant like Tycho and a core-collapse remnant like Cas A.
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