Hybridization may drive rare taxa to extinction through genetic swamping, where the rare form is replaced by hybrids, or by demographic swamping, where population growth rates are reduced due to the wasteful production of maladaptive hybrids. Conversely, hybridization may rescue the viability of small, inbred populations. Understanding the factors that contribute to destructive versus constructive outcomes of hybridization is key to managing conservation concerns. Here, we survey the literature for studies of hybridization and extinction to identify the ecological, evolutionary, and genetic factors that critically affect extinction risk through hybridization. We find that while extinction risk is highly situation dependent, genetic swamping is much more frequent than demographic swamping. In addition, human involvement is associated with increased risk and high reproductive isolation with reduced risk. Although climate change is predicted to increase the risk of hybridization‐induced extinction, we find little empirical support for this prediction. Similarly, theoretical and experimental studies imply that genetic rescue through hybridization may be equally or more probable than demographic swamping, but our literature survey failed to support this claim. We conclude that halting the introduction of hybridization‐prone exotics and restoring mature and diverse habitats that are resistant to hybrid establishment should be management priorities.