The origin of novelty is a critical subject for evolutionary biologists. Early geneticists speculated about the sudden appearance of new species via special macromutations, epitomized by Goldschmidt’s infamous “hopeful monster”. Although these ideas were easily dismissed by the insights of the Modern Synthesis, a lingering fascination with the possibility of sudden, dramatic change has persisted. Recent work on hybridization and gene exchange suggests an underappreciated mechanism for the sudden appearance of evolutionary novelty that is entirely consistent with the principles of modern population genetics. Genetic recombination in hybrids can produce transgressive phenotypes, “monstrous” phenotypes beyond the range of parental populations. Transgressive phenotypes can be products of epistatic interactions or additive effects of multiple recombined loci. We compare several epistatic and additive models of transgressive segregation in hybrids and find that they are special cases of a general, classic quantitative genetic model. The Dobzhansky-Muller model predicts “hopeless” monsters, sterile and inviable transgressive phenotypes. The Bateson model predicts “hopeful” monsters with fitness greater than either parental population. The complementation model predicts both. Transgressive segregation after hybridization can rapidly produce novel phenotypes by recombining multiple loci simultaneously. Admixed populations will also produce many similar recombinant phenotypes at the same time, increasing the probability that recombinant “hopeful monsters” will establish true-breeding evolutionary lineages. Recombination is not the only (or even most common) process generating evolutionary novelty, but might be the most credible mechanism for sudden appearance of new forms DOI: 10.1007/s11692-012-9209-