Terrestrial weeds continue to evolve in association with the rapid global changes in our land-use systems,due to their regenerative strategies, their adaptability to change, and their inherent diversity. Currently,invasive weeds are estimated to cost the United States' economy up to $35 billion per year, and this total is rapidly increasing, as greater numbers of invasive species become naturalized. Several invasive exoticspecies have more recently established across New York State, creating difficulties for agricultural producers,roadside and natural areas managers, and homeowners and resulting in millions of dollars expended annually for their control. Three perennials that have become particularly problematic in New York State in recent years in both agricultural and roadside settings include Japanese knotweed (Polygonum cuspidatumSieb. & Zucc.), mugwort (Artemisia vulgaris L.), and pale swallow-wort (Vincetoxicum rossicum(Kleop.) Barbar.). This review describes their history, biology, ecology, and potential for management and focuses on key characteristics contributing to their spread in New York State and adjacent regions.