Species charisma, understood as a set of species characteristics and their perception that affect people's attitudes and behaviors, is a highly relevant concept for invasion science, with implications across all stages of the invasion process. However, the concept of invasive alien species (IAS) charisma has not yet been systematically investigated. Here, we discuss this concept, provide a set of recommendations for further research and highlight management implications. We review how charisma affects the processes associated with biological invasions and IAS management, including: effects on species introductions and spread, media portrayals, public perceptions of species management, research attention, and active public involvement in research and management. Explicit consideration of IAS charisma is critical to improve understanding of the drivers of people's attitudes towards particular IAS and planned management measures and strategies, and to implement programs aiming to influence stakeholder perceptions and behavior and to strengthen public engagement. In a nutshell • We discuss the concept of charismatic invasive alien species (IAS), highlight management implications and provide a set of recommendations for further research. • The charisma of IAS might influence all stages of the invasion process, and both charisma and its influence can vary over time and space. • It is a potential hindrance to management actions by affecting public support and contributing to conflicts. • We explore the concept of IAS charisma and its effects on biological invasions and management, including species introductions, media portrayal, public perceptions, opposition to management, research effort and public participation in research and management.