Invasive nonindigenous plant species (NIPS) threaten native diversity, alter ecosystem processes, and may interact with other components of global environmental change. Here, a general framework is outlined that attempts to connect patterns of plant invasion to processes underlying these patterns at four well-established spatio-temporal stages of the invasion process: transport, colonization, establishment, and landscape spread. At each stage we organize findings and ideas about the filters that limit NIPS success and the interaction of these filters with historical aspects of introduction events, NIPS traits, and ecosystem properties. While it remains difficult to draw conclusions about the risk of invasion across ecosystems, to delineate universal 'invader traits', or to predict large-scale extinctions following invasions, this review highlights the growing body of research that suggests that the success of invasive NIPS is controlled by a series of key processes or filters. These filters are common to all invasion events, and will interact throughout the stages of plant invasion, although the relative importance of a filter may be stage, species or location specific. It is suggested that both research and management programs may benefit from employing multiscale and stage approaches to studying and controlling invasion. We further use the framework to briefly examine potential interactions between climate change and filters that limit NIPS invasion.