Asteraceae, the largest family of flowering plants, has given rise to many notorious invasive species. Using publicly available transcriptome assemblies from 35 Asteraceae, including six major invasive species, we examined evidence for micro- and macro-evolutionary genomic changes associated with invasion. To detect episodes of positive selection repeated across multiple introductions, we conducted comparisons between native and introduced genotypes from six focal species and identified genes with elevated rates of amino acid change (dN/dS). We then looked for evidence of positive selection at a broader phylogenetic scale across all taxa. As invasive species may experience founder events during colonization and spread, we also looked for evidence of increased genetic load in introduced genotypes. We rarely found evidence for parallel changes in orthologous genes in the intraspecific comparisons, but in some cases we identified changes in members of the same gene family. Using among-species comparisons, we detected positive selection in 0.003–0.69% and 2.4–7.8% of the genes using site and stochastic branch-site models, respectively. These genes had diverse putative functions, including defence response, stress response and herbicide resistance, although there was no clear pattern in the GO terms. There was no indication that introduced genotypes have a higher proportion of deleterious alleles than native genotypes in the six focal species, suggesting multiple introductions and admixture mitigated the impact of drift. Our findings provide little evidence for common genomic responses in invasive taxa of the Asteraceae and hence suggest that multiple evolutionary pathways may lead to adaptation during introduction and spread in these species.