Eradication and maintenance management of invasive species have long histories, and incremental improvement of existing technologies plus occasional novel approaches have led to more challenging targets and impressive successes, especially on islands. Many nonnative mammals and several nonnative birds, insects, and plants have been eradicated from islands. Islands over 10,000 ha are often now feasible targets. Eradication trends include more frequent attempts, and higher success rates, on larger islands and inhabited islands as well as projects targeting multiple invasive species. Insect and plant invaders on both continents and islands have been maintained at low densities by biological control, and plants have been controlled short of eradication by herbicides, often combined with physical or mechanical means. Failures in both eradication and maintenance management often result from insufficient long-term commitment of resources. Excitement and controversy abound over the prospect that new techniques relying on molecular genetic tools – especially RNA-guided gene drives but also including RNA interference – may permit eradication or maintenance management of nonnative invaders in some situations that have previously appeared extremely difficult or infeasible.