Invasion genetics is a relatively new discipline that investigates patterns of genetic variation in populations of invasive species and their ecological and evolutionary consequences. Evolutionary biologists have a long-standing interest in colonizing species, owing to their short life cycles and widespread distributions, but not until publication of The Genetics of Colonizing Species (1965), edited by H.G. Baker and G.L. Stebbins, was a synthesis on the genetics and evolution of colonizers available. Here, I make the case that the Baker and Stebbins volume is the foundational document for invasion genetics, and in conjunction with the increased use of genetic markers and development of invasion biology, resulted in the birth of this new field over the past two decades. I consider the historical origins and legacy of the Baker and Stebbins volume and review some of the key issues that were addressed. I provide biographical sketches of the two editors, emphasizing their contrasting backgrounds and personalities. I review examples from my own work on plant invasions that are relevant to issues discussed by contributors to the volume. These include the following: determinants of invasion success, life history trade-offs, generalist vs. specialist strategies, general-purpose genotypes, adaptive phenotypic plasticity, mating systems and the influence of bottlenecks on genetic variation. I conclude by posing several key questions in invasion genetics and argue that one of the main challenges that the area faces is to integrate experimental field studies of the ecology and demography of populations with the largely descriptive approaches that have tended to dominate most research to date.