Plant invasions often involve rapid evolutionary changes. Founder effects, hybridization, and adaptation to novel environments cause genetic differentiation between native and introduced populations, contributing to the success of invaders. The Evolution of Increased Competitive Ability (EICA) hypothesis suggests that after enemy release, plants evolve to be less defended but more competitive, increasing vigor in introduced populations. Comparative studies of native versus introduced populations are needed to detect evolutionary change. Field data show increased vigor and reduced herbivory in introduced populations. Molecular studies show genetic diversity in introduced populations is not consistently different from native populations. Multiple introductions are common. In common garden studies, introduced populations often show increased growth or decreased resistance. However, few fully test the EICA hypothesis by addressing growth and defense in the same species. Overall, there is reasonable empirical evidence that genetic differentiation through rapid evolutionary change is important in plant invasions. Conceptual and methodological issues in cross-continental comparisons are discussed, with recommendations for future research. Testing EICA should emphasize competitive ability and plant tolerance. Other characteristics than defense and growth may also play a role in plant invasions. Biological invasions are a major threat to global biodiversity. Research on their causes and consequences has been limited, revealing insufficient understanding of population dynamics, ecological interactions, and ecosystem stability. Evolution can be rapid and relevant to ecological studies. Invasive species may evolve due to genetic drift, hybridization, or changes in selection regimes. Many invasive species become abundant after a lag time, possibly after evolutionary adjustments. Invasive species may provide good models for studying rapid evolution. The EICA hypothesis proposes that after enemy release, plants evolve greater vigor. If there is a trade-off between resource allocation to growth and defense, natural selection favors less defended but more competitive genotypes in introduced ranges. Defense and competitive ability are important characteristics of invasive plants, but not the only ones. Other hypotheses about evolutionary change in invasive plants are possible. Genetic differentiation in introduced populations may occur in any ecological trait beneficial under novel selection conditions. Testing hypotheses about adaptive evolutionary change involves comparing offspring from native and introduced populations in a common environment. If native and introduced populations differ significantly in ecological characteristics under identical conditions, this is evidence for genetic differentiation. Neutral genetic variation among and between native and introduced populations can be analyzed with DNA markers or allozymes. Molecular markers are important tools in plant invasions, providing information about invasion pathways and genetic variation. Genetic differentiation among populations is lower in introduced ranges in many studies. Multiple introductions are common, especially in North America. Molecular data are important for choosing appropriate controls in common garden studies and interpreting their results. Comparisons of quantitative traits in a common environment show increased growth in many studies and decreased resistance in others. Only 19 studies fully tested the EICA hypothesis by addressing both growth and defense. Eight of these found support for EICA. The EICA hypothesis predicts increased growth and decreased resistance in introduced populations. Overall, there is moderate support for EICA. However,Plant invasions often involve rapid evolutionary changes. Founder effects, hybridization, and adaptation to novel environments cause genetic differentiation between native and introduced populations, contributing to the success of invaders. The Evolution of Increased Competitive Ability (EICA) hypothesis suggests that after enemy release, plants evolve to be less defended but more competitive, increasing vigor in introduced populations. Comparative studies of native versus introduced populations are needed to detect evolutionary change. Field data show increased vigor and reduced herbivory in introduced populations. Molecular studies show genetic diversity in introduced populations is not consistently different from native populations. Multiple introductions are common. In common garden studies, introduced populations often show increased growth or decreased resistance. However, few fully test the EICA hypothesis by addressing growth and defense in the same species. Overall, there is reasonable empirical evidence that genetic differentiation through rapid evolutionary change is important in plant invasions. Conceptual and methodological issues in cross-continental comparisons are discussed, with recommendations for future research. Testing EICA should emphasize competitive ability and plant tolerance. Other characteristics than defense and growth may also play a role in plant invasions. Biological invasions are a major threat to global biodiversity. Research on their causes and consequences has been limited, revealing insufficient understanding of population dynamics, ecological interactions, and ecosystem stability. Evolution can be rapid and relevant to ecological studies. Invasive species may evolve due to genetic drift, hybridization, or changes in selection regimes. Many invasive species become abundant after a lag time, possibly after evolutionary adjustments. Invasive species may provide good models for studying rapid evolution. The EICA hypothesis proposes that after enemy release, plants evolve greater vigor. If there is a trade-off between resource allocation to growth and defense, natural selection favors less defended but more competitive genotypes in introduced ranges. Defense and competitive ability are important characteristics of invasive plants, but not the only ones. Other hypotheses about evolutionary change in invasive plants are possible. Genetic differentiation in introduced populations may occur in any ecological trait beneficial under novel selection conditions. Testing hypotheses about adaptive evolutionary change involves comparing offspring from native and introduced populations in a common environment. If native and introduced populations differ significantly in ecological characteristics under identical conditions, this is evidence for genetic differentiation. Neutral genetic variation among and between native and introduced populations can be analyzed with DNA markers or allozymes. Molecular markers are important tools in plant invasions, providing information about invasion pathways and genetic variation. Genetic differentiation among populations is lower in introduced ranges in many studies. Multiple introductions are common, especially in North America. Molecular data are important for choosing appropriate controls in common garden studies and interpreting their results. Comparisons of quantitative traits in a common environment show increased growth in many studies and decreased resistance in others. Only 19 studies fully tested the EICA hypothesis by addressing both growth and defense. Eight of these found support for EICA. The EICA hypothesis predicts increased growth and decreased resistance in introduced populations. Overall, there is moderate support for EICA. However,