A new Task Force within the COST-SMARTER has recently been created. This group is composed of population genetics experts from five European countries in charge of focusing on “Genetics on Ambrosia” (Austria, France, Germany, Hungary, Sweden). Their mission was to review molecular methods used in published genetics studies on common ragweed and to discuss about future projects. Two different types of molecular markers are generally used in the literature to investigate the genetic structure within and between introduced and/or native populations of common ragweed: microsatellite markers and amplified fragment length polymorphism (AFLP). These methods permit the researchers to trace-back the common ragweed invasion history and its worldwide spread as well as to identify certain evolutionary processes like selection, adaptation or genetic bottleneck due to introduction. One common conclusion is the presence of two main genetic clusters within Europe coming from two different regions of the native range. However, this conclusion is based on a limited number of microsatellite markers used (12 nuclear + 4 plastid). New methods using haplotype analysis or selected markers present on functional parts of the genome (i.e., related to herbicide-resistance) should be more investigated in order to increase the knowledge on common ragweed. Transcriptomic analyses are starting to be employed in USA to observe gene expression related to adaptations and identify the genes of the “invasiveness”. These new methods will now be promoted within the different European projects in order to open the way of whole-genome sequencing of Ambrosia artemisiifolia in the future.