AbstractA diverse array of molecular markers and constantly evolving analytical approaches have been employed to reconstruct the invasion histories of the most notorious invasions. Detailed information on the source(s) of introduction, invasion route, type of vectors, number of independent introductions and pathways of secondary spread has been corroborated for a large number of biological invasions. In this review, I present the promises and limitations of current techniques while discussing future directions. Broad phylogeographic surveys of native and introduced populations have traced back invasion routes with surprising precision. These approaches often further clarify species boundaries and reveal complex patterns of genetic relationships with noninvasive relatives. Moreover, fine‐scale analyses of population genetics or genomics allow deep inferences on the colonization dynamics across invaded ranges and can reveal the extent of gene flow among populations across various geographical scales, major demographic events such as genetic bottlenecks as well as other important evolutionary events such as hybridization with native taxa, inbreeding and selective sweeps. Genetic data have been often corroborated successfully with historical, geographical and ecological data to enable a comprehensive reconstruction of the invasion process. The advent of next‐generation sequencing, along with the availability of extensive databases of repository sequences generated by barcoding projects opens the opportunity to broadly monitor biodiversity, to identify early invasions and to quantify failed invasions that would otherwise remain inconspicuous to the human eye.