Invasive species are of great interest to evolutionary biologists and ecologists because they represent historical examples of dramatic evolutionary and ecological change.  Likewise, they are increasingly important economically and environmentally as pests.  Obtaining generalizations about the tiny fraction of immigrant taxa that become successful invaders has been frustrated by two enigmatic phenomena.  Many of those species that become successful only do so (i) after an unusually long lag time after initial arrival,and/or (ii) after multiple introductions.  We propose an evolutionary mechanism that may account for these observations.  Hybridization between species or between disparate source populations may serve as a stimulus for the evolution of invasiveness.  We present and review a remarkable number of cases in which hybridization preceded the emergence of successful invasive populations. Progeny with a history of hybridization may enjoy one or more potential genetic benefits relative to their progenitors.  The observed lag times and multiple introductions that seem a prerequisite for certain species to evolve invasiveness may be a correlate of the time necessary for previously isolated populations to come into contact and for hybridization to occur.  Our examples demonstrate that invasiveness can evolve.  Our model does not represent the only evolutionary pathway to invasiveness, but is clearly an underappreciated mechanism worthy of more consideration in explaining the evolution of invasiveness in plants.