The Anthropocene Epoch is characterized by novel and increasingly complex dependencies between the environment and human civilization, with many challenges of biodiversity management emerging as wicked problems. Problems arising from the management of biological invasions can be either tame (with simple or obvious solutions) or wicked, where difficulty in appropriately defining the problem can make complete solutions impossible to find. We review four case studies that reflect the main goals in the management of biological invasions -prevention, eradication, and impact reduction -assessing the drivers and extent of wickedness in each. We find that a disconnect between the perception and reality of how wicked a problem is can profoundly influence the likelihood of successful management. For example, managing species introductions can be wicked, but shifting from species-focused to vector-focused risk management can greatly reduce the complexity, making it a tame problem. The scope and scale of the overall management goal will also dictate the wickedness of the problem and the achievability of management solutions (cf. eradication and ecosystem restoration). Finally, managing species that have both positive and negative impacts requires engagement with all stakeholders and scenario-based planning. Effective management of invasions requires either recognizing unavoidable wickedness, or circumventing it by seeking alternative management perspectives.