The number of non-native plant species established outside of cultivation in the New Zealand archipelago is higher than for any other islands worldwide. Faced with this scale of plant invasions, there has been considerable investment in the scientific and operational aspects of prevention, eradication and control. As a result, New Zealand is ideally placed to illustrate the many challenges that plant invasions present worldwide as well as the possible solutions. New Zealand has been at the forefront of biosecurity policy developments to tackle plant invasions being one of the first countries to: (a) implement national legislation to address the management of non-native plants; (b) establish a national permitted list (white-list) for plant imports; and (c) introduce bans on the sale, distribution, or propagation of non-native plant species. However, these preventative measure are only effective where there are also adequate border inspection regimes, compliance monitoring of the horticulture industry, and surveillance of internet trade. While New Zealand has successfully eradicated several non-native plant species from its territory, the small number of successes reflects the short-term, local and often uncoordinated efforts to manage non-native plants rather than national programmes backed by legislation and financed over several decades. New Zealand supports a world-leading biological control programme, but this has led to sustained, large-scale control for only a handful of species. In natural areas, most management attempts using mechanical or herbicide treatments have failed to achieve control and there has been a progressive reduction in the area, and frequency of these programmes over time. This is illustrative of the challenges facing those responsible for managing non-native plants in any region of the world. A general insight is that a shift in mindset is required that overcomes significant cognitive biases that include succumbing to the pressure to always intervene, underestimating the non-linear trajectories of invasions, failing to articulate the values at stake, and underestimating the time programmes require to succeed. Important lessons of global relevance include the need for managers to: (a) recognise when and where sleeper weeds are likely to become a national issue, especially as a result of climate change; (b) quantify impacts on those values that stakeholders most cherish rather than those that are easy to measure; (c) provide accurate estimates of the potential future extent of the invasion in the absence of management; and (d) identify clear indicators of successful progress over the course of a long-term management programme.