Some exploding stars (supernovae) are powerful emitters of centimeter radio radiation. Detailed observations have shown that these supernovae quickly become detectable in the radio range, first at shorter wavelengths (higher frequencies) and later at progressively longer and longer wavelengths (lower frequencies). This part of the phenomenon appears to be well explained by a monotonic decrease in the amount of ionized material surrounding the radio-emitting regions as the shock from the explosion travels outward. The radio emission itself is of a nonthermal, synchrotron origin, as is the case in most bright cosmic radio sources. Once the absorption effects become negligible, the radio intensity declines with time until reaching the detection limit of the telescope. Models suggest that the absorbing material originates in a dense wind of matter lost by the supernova progenitor star, or by its companion if it is in a binary system, in the last stages of evolution before the explosion. The synchrotron radio emission can be generated either externally by the shock wave from the explosion propagating through this same high density stellar wind or internally by a rapidly rotating neutron star, which is the collapsed core of the exploded star. Present results appear to favor the former model for at least the first several years after the supernova explosion, although the latter model remains viable.