We review the state of the art of alien plant research with emphasis on conceptual advances and knowledge gains on general patterns and drivers, biotic interactions, and evolution. Major advances include the identification of different invasion stages and invasiveness dimensions (geographic range, habitat specificity, local abundance) and the identification of appropriate comparators while accounting for propagule pressure and year of introduction. Developments in phylogenetic and functional trait research bear great promise for better understanding of the underlying mechanisms. Global patterns are emerging with propagule pressure, disturbance, increased resource availability, and climate matching as major invasion drivers, but species characteristics also play a role. Biotic interactions with resident communities shape invasion outcomes, with major roles for species diversity, enemies, novel weapons, and mutualists. Mounting evidence has been found for rapid evolution of invasive aliens and evolutionary responses of natives, but a mechanistic understanding requires tighter integration of molecular and phenotypic approaches. We hope the open questions identified in this review will stimulate further research on the ecology and evolution of alien plants.