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The shock between the colliding winds in binary systems containing two massive stars accelerates particles to relativistic energies. These energetic particles can produce observable non-thermal radiation from the radio to γ-rays. The important physical processes in such systems are very similar to those we have proposed for non-thermal emissions from single hot stars, which have shocks generated by instabilities in the radiatively driven stellar winds. This paper discusses the theory and observations of non-thermal radiation in the radio, X-ray, and γ-ray regions from both single stars and massive binaries. Similarities and differences between the two types of systems are outlined. We discuss two important physical effects that apparently have been neglected in previous theoretical work on colliding wind binaries.