Species of the genus Centaurea, members of the Asteraceae that invaded North America a century ago, have been identified as major problems for rangelands and forests, occupying millions of hectares of land and incurring substantial control costs and grass production losses.  While intensively studied, diffuse (C. diffusa) and spotted knapweed (C. stoebe) remain an apparent enigma to researchers and managers.  The plants have been reported to be invulnerable to sustainable management approaches that have succeeded for other invasive plants in western North America.  Here, we review findings on top-down (herbivore) impacts and bottom-up (plant competition and resource availability) effects, report our own work, and suggest that current views on knapweed responses to these manipulations have been strongly influenced by the experimental design and environmental context of these studies.  Concurrent application of top-down and bottom-up constraints appears to have strong, negative impacts on the dominance of these species.  Massive reductions in densities of C. diffusa have already been reported throughout western North America, and the approach appears to be having a similar effect on C. stoebe.