The Asian tiger mosquito Aedes albopictus is currently one of the most threatening invasive species in the world. Native to Southeast Asia, the species has spread throughout the world in the past 30 years and is now present in every continent but Antarctica. Because it was the main vector of recent Dengue and Chikungunya outbreaks, and because of its competency for numerous other viruses and pathogens such as the Zika virus, A. albopictus stands out as a model species for invasive diseases vector studies. A synthesis of the current knowledge about the genetic diversity of A. albopictus is needed, knowing the interplays between the vector, the pathogens, the environment and their epidemiological consequences. Such resources are also valuable for assessing the role of genetic diversity in the invasive success. We review here the large but sometimes dispersed literature about the population genetics of A. albopictus. We first debate about the experimental design of these studies and present an up-to-date assessment of the available molecular markers. We then summarize the main genetic characteristics of natural populations and synthesize the available data regarding the worldwide structuring of the vector. Finally, we pinpoint the gaps that remain to be addressed and suggest possible research directions.