Abstract Herbert Baker arguably initiated the search for species characteristics determining alien plant invasion success, with his formulation of the ‘ideal weed’. Today, a profusion of studies has tested a myriad of traits for their importance in explaining success of alien plants, but the multiple, not always appropriate, approaches used have led to some confusion and criticism. We argue that a greater understanding of the characteristics explaining alien plant success requires a refined approach that respects the multistage, multiscale nature of the invasion process. We present a schema of questions we can ask regarding the success of alien species, with the answering of one question in the schema being conditional on the answer of preceding questions (thus acknowledging the nested nature of invasion stages). For each question, we identify traits and attributes of species we believe are likely to be most important in explaining species success, and we make predictions as to how we expect successful aliens to differ from natives and from unsuccessful aliens in their characteristics. We organize the findings of empirical studies according to the questions in our schema that they have addressed, to assess the extent to which they support our predictions. We believe that research on plant traits of alien species has already told us a lot about why some alien species become successful after introduction. However, if we ask the right questions at the appropriate scale and use appropriate comparators, research on traits may tell us whether they are really important or not, and if so under which conditions.