The rate at which plant invasions occur is accelerating globally, and a growing amount of recent research uses genetic analysis of invasive plant populations to better understand the histories, processes, and effects of plant invasions. The goal of this review is to provide natural resource managers with an introduction to this research. We discuss examples selected from published studies that examine intraspecific genetic diversity and the role of hybridization in plant invasion. We also consider the conflicting evidence that has emerged from recent research for the evolution of increased competitiveness as an explanation for invasion, and the significance of multiple genetic characteristics and patterns of genetic diversity reported in the literature across different species invasions. High and low levels of genetic diversity have been found in different invading plant populations, suggesting that either selection leading to local adaptation, or pre-adapted characteristics such as phenotypic plasticity, can lead to aggressive range expansion by colonizing nonnative species. As molecular techniques for detecting hybrids advance, it is also becoming clear that hybridization is a significant component of some plant invasions, with consequences that include increased genetic diversity within an invasive species, generation of successful novel genotypes, and genetic swamping of native plant gene pools. Genetic analysis of invasive plant populations has many applications, including predicting population response to biological or chemical control measures based on diversity levels, identifying source populations, tracking introduction routes, and elucidating mechanisms of local spread and adaptation. This information can be invaluable in developing more effectively targeted strategies for managing existing plant invasions and preventing new ones. Future genetic research, including the use of high throughput molecular marker systems and genomic approaches such as microarray analysis, has the potential to contribute to better understanding and more effective management of plant invasions.