Abstract. Humans are the most invasive of vertebrates and they have taken many plants and animals with them to colonise new environments. This has been particularly so in Australasia, where Laurasian and domesticated taxa have collided with ancient Gondwanan ecosystems isolated since the Eocene Epoch. Many plants and animals that humans introduced benefited from their pre-adaptation to their new environments and some became invasive, damaging the biodiversity and agricultural value of the invaded ecosystems. The invasion of non-native organisms is accelerating with human population growth and globalisation. Expansion of trade has seen increases in purposeful and accidental introductions, and their negative impacts are regarded as second only to activities associated with human population growth. Here, the theoretical processes, economic and environmental costs of invasive alien species (i.e. weeds and vertebrate pests) are outlined. However, defining the problem is only one side of the coin. We review some theoretical underpinnings of invasive species science and management, and discuss hypotheses to explain successful biological invasions. We consider desired restoration states and outline a practical working framework for managing invasive plants and animals to restore, regenerate and revegetate invaded Australasian ecosystems.Additional keywords: adaptive management, biological invasions, removal, rate of increase.