Evolution can occur over contemporary timescales, which may be crucial for the invasive success of non-native plant species. Many studies have shown rapid evolution by comparing native and non-native populations in common gardens. However, our understanding of the mechanisms underpinning rapid evolution is still incomplete. Here, we identify the progress, applications, and limitations of studies on rapid evolution of non-native plants with respect to sampling, experimental design and experimental methods. To encompass broad variation within and between the ranges, we recommend sampling across large-scale environmental gradients. We also suggest careful consideration of pitfalls related to the choice of seed families and of the biotic interaction under focus. The latter should be chosen with a view on both the experimental treatment and the corresponding field data to estimate population history. Furthermore, we suggest exploiting multiple omics approaches to address the complexity of biotic interactions, and to account for non-adaptive evolution with molecular data on demographic history of populations. We also reviewed papers that studied rapid evolution in non-native plants and quantified how many of these met our criteria. We anticipate that disentangling adaptive and non-adaptive drivers of among-population variation can increase the accuracy of research on rapid evolution, and that integrating phenotypic, metabolomic and population genomic data can bring opportunities for studying complex biotic interactions. We also illustrate the importance of large collaborative networks and present our scientific network iCONNECT (integrative CONyza NEtwork for Contemporary Trait evolution), with the goal of motivating similar studies on the mechanistic understanding of rapid evolution.