Marine invasive macroalgae can have severe local-scale impacts on ecological communities. The kelp Undaria pinnatifida is one of the most successful marine invasive species worldwide, and is widely regarded as one of the worst. Here, we review research on Undaria in Australasia, where the kelp is established throughout much of New Zealand and south-eastern Australia. The presence of Undaria for at least three decades in these locations makes Australasia one of the longest-invaded bioregions globally, and a valuable case study for considering Undaria's invasion success and associated impacts. In Australasia, Undaria has primarily invaded open spaces, turf communities, and gaps in native canopies within a relatively narrow elevation band on rocky shores. Despite its high biomass, Undaria has relatively few direct impacts on native species, and can increase community-wide attributes such as primary productivity and the provision of biogenic habitat. Therefore, Australasian Undaria research provides an example of a decoupling between the success and impact of an invasive species. Undaria will most likely continue to spread along thousands of kilometres of rocky coastline in temperate Australasia, due to its tolerance to large variations in temperature, ability to exploit disturbances to local communities, and the continued transfer among regions via vessel movements and aquaculture activities. However, the spread of Undaria remains difficult to manage as eradication is challenging and seldom successful. Therefore, understanding potential invasion pathways, maintaining native canopy-forming species that limit Undaria success, and effectively managing anthropogenic vectors of Undaria spread, should be key management priorities.