Abstract A review is made of the success of naturalised plants grouped as plateau, increasing, fluctuating, or declining species. Most of the plentiful plateau species established at an early date and are more predictable in behaviour than the recent minor aliens which, in the short term, appear to be maintaining steady numbers. Increasing species are mainly recent garden escapes with high weed potential. Species with fluctuating populations have varying opportunity to establish and flourish, or an apparent inherent inability to maintain steady numbers. Declining species are mostly in diminishing habitats. Successful plants are considered to include those which aggressively suppress, those which can coexist and maintain populations, and those which can occupy temporary or difficult habitats. High levels of success are aided by competitive ability, quick maturity, and recovery from mutilation. Prolific seeding and efficient dispersal are helpful features but are lacking in many successful species. Cloning ...