Many emerging invasive species display evidence of rapid adaptation. Contemporary genetic studies demonstrate that adaptation to novel environments can occur within 20 generations or less, indicating that evolutionary processes can influence invasiveness. However, the source of genetic or epigenetic variation underlying these changes remains uncharacterised. Here, we review the potential for rapid adaptation from standing genetic variation and from new mutations, and examine four types of evolutionary change that might promote or constrain rapid adaptation during the invasion process. Understanding the source of variation that contributes to adaptive evolution in invasive plants is important for predicting future invasion scenarios, identifying candidate genes involved in invasiveness, and, more generally, for understanding how populations can evolve rapidly in response to novel and changing environments.