In addition to being a major threat to biodiversity and ecosystem functioning, biological invasions also have profound impacts on economies and human wellbeing. However, the threats posed by invasive species often do not receive adequate attention and lack targeted management. In part, this may result from different or even ambivalent perceptions of invasive species which have a dual effect for stakeholders—being simultaneously a benefit and a burden. For these species, literature that synthesizes best practice is very limited, and analyses providing a comprehensive understanding of their economics are generally lacking. This has resulted in a critical gap in our understanding of the underlying trade-offs surrounding management efforts and approaches. Here, we explore qualitative trends in the literature for invasive species with dual effects, drawing from both the recently compiled InvaCost database and international case studies. The few invasive species with dual roles in InvaCost provide evidence for a temporal increase in reporting of costs, but with benefits relatively sporadically reported alongside costs. We discuss methods, management, assessment and policy frameworks dedicated to these species, along with lessons learned, complexities and persisting knowledge gaps. Our analysis points at the need to enhance scientific understanding of those species through inter- and cross-disciplinary efforts that can help advance their management.