My first new moth for a while, a Light Brown Apple Moth (#317), is originally a native of Australia.  First found in UK in the 1930s it's now spread across much of England making a pest of itself in orchards and gardens.  Similarly, it's been accidentally introduced to New Zealand, New Caledonia, Hawaii and California.  In Australia the population is kept under control naturally by insect predators, especially parasitic wasps and flies, that eat the larvae.  However in other countries these predators are not present, so the moths can become a significant pest in orchards.  It's an interesting reversal of all the non-native plants and animals introduced (often deliberately) to Australia and New Zealand by European colonists, which now have to be controlled at great cost by local farmers and conservationists.