Invasive plants often appear to be more competitive than native species, but there have been few tests of this hypothesis. We reviewed published pair-wise experiments between invading and native plant species. Although the designs that have been used allow only limited inferences, the available data suggest that the effect of invasive species on native species is usually stronger than vice versa. Furthermore, mixtures of invasive and native species are generally less productive than monocultures of the native species, but not less than monocultures of the invasive species. However, the selection of invaders and natives for study has not been random, and the data could be biased towards highly competitive invaders and natives that are weaker than average competitors. We attempt to clarify confusion surrounding the concept of competitive superiority in the context of plant invasions, and we discuss the limitations of the methods that have been used to investigate competition between invasive and native species. To rigorously test the generality of the hypothesis that invaders are better competitors than natives we need to compare the effects of closely related native and invasive species on each other. We suggest that the influence of an invading species on total plant community biomass is an important clue in understanding the role of competition in a plant invasion. The role of competition in the establishment and naturalization stages of the invasion process may be very different from its role in the "outbreak" stage.