Although freshwater invasions have not been targeted for maintenance management or eradication as often as terrestrial invasions have, attempts to do so are frequent. Failures as well as successes abound, but several methods have been improved and new approaches are on the horizon. Many freshwater fish and plant invaders have been eliminated, especially by chemical and physical methods for fishes and herbicides for plants. Efforts to maintain invasive freshwater fishes at low levels have sometimes succeeded, although continuing the effort has proven challenging. By contrast, successful maintenance management of invasive freshwater plants is uncommon, although populations of several species have been managed by biological control. Invasive crayfish populations have rarely been controlled for long. Marine invasions have proven far less tractable than those in fresh water, with a few striking eradications of species detected before they had spread widely, and no marine invasions have been substantially managed for long at low levels. The rapid development of technologies based on genetics has engendered excitement about possibly eradicating or controlling terrestrial invaders, and such technologies may also prove useful for certain aquatic invaders. Methods of particular interest, alone or in various combinations, are gene-silencing, RNA-guided gene drives, and the use of transgenes. © Springer Nature Switzerland AG 2020.