Natural hybridization between closely related taxa is a common phenomenon in both plants and animals. Hybridization has often been viewed as a destructive force that could erode established gene pools, but it is increasingly being recognized as a potentially creative force in evolution because it can lead to a mixture of novel genotypes, some of which have the potential for rapid adaptation to new environmental conditions. However, the evolutionary dynamics leading to the emergence of newly adapted gene pools after hybridization are largely unexplored. Here, we argue that the identification and analysis of the dynamic processes that occur after the first contact deserve specific attention, because this is the phase where hybrid speciation is most different from other forms of speciation.