AbstractThe presence of alien species represents a major cause of habitat degradation and biodiversity loss worldwide, constituting a critical environmental challenge of our time. Despite sometimes experiencing reduced propagule pressure, leading to a reduced genetic diversity and an increased chance of inbreeding depression, alien invaders are often able to thrive in the habitats of introduction, giving rise to the so‐called “genetic paradox” of biological invasions. The adaptation of alien species to the new habitats is therefore a complex aspect of biological invasions, encompassing genetic, epigenetic, and ecological processes. Albeit numerous studies and reviews investigated the mechanistic foundation of the invaders' success, and aimed to solve the genetic paradox, still remains a crucial oversight regarding the temporal context in which adaptation takes place. Given the profound knowledge and management implications, this neglected aspect of invasion biology should receive more attention when examining invaders' ability to thrive in the habitats of introduction. Here, we discuss the adaptation mechanisms exhibited by alien species with the purpose of highlighting the timing of their occurrence during the invasion process. We analyze each stage of the invasion separately, providing evidence that adaptation mechanisms play a role in all of them. However, these mechanisms vary across the different stages of invasion, and are also influenced by other factors, such as the transport speed, the reproduction type of the invader, and the presence of human interventions. Finally, we provide insights into the implications for management, and identify knowledge gaps, suggesting avenues for future research that can shed light on species adaptability. This, in turn, will contribute to a more comprehensive understanding of biological invasions.