Supernova explosions inside preexisting wind-driven bubbles create composite remnants, and their evolution is defined by the bubble structure. The ejecta expand almost untouched until they interact with the cool and dense external shell, after which they experience a rapid thermalization. The interaction generates optical and X-ray emission and reaccelerates the former wind-driven shell. This early radiative phase, which may be responsible for the optical emission of some historical remnants, can be dominant and can define the rest of the evolutionary path. If the mass of the shell is smaller than about 50 M., radiative losses represent only a small fraction of the exposion energy and the remnant enters into a quasi-adiabatic track. In this case the outgoing shock can overrun the whole shell and propagate into the undisturbed ambient medium, creating a multishell structure. For larger shell masses, radiative losses drive the evolution directly into the momentum conserving stage, and the Sedov phase is inhibited. When the ejecta contain high-density fragments, their impacts can puncture the shell, enhance the early emission, and drive a series of new shocks into the unperturbed medium. These shocks create a very complex (and turbulent) remnant with an X-ray outer rim. Thus, in the case of either fragmented or unfragmented ejecta, the resulting remnants have a complex structure, and they age faster than those evolving in a constant density medium. These results provide an appropriate scheme to analyze the observed properties of actual remnants.
