The Anthropocene is characterised by a continuous human-mediated reshuffling of the distributions of species globally. Both intentional and unintentional introductions have resulted in numerous species being translocated beyond their native ranges, often leading to their establishment and subsequent spread - a process referred to as biological invasion. Biological invasions are associated with profound changes in the composition, structure, and functioning of recipient ecosystems, plus substantial financial losses and disruptions to society, culture, and human well-being. These ecological, economic, and socio-cultural impacts are interrelated, ubiquitous, and detrimental, yet they are often subjectively perceived or inaccurately quantified. Persistent knowledge gaps remain, however, which limit our understanding of the complex and multifaceted causes and mechanisms of invasion impacts. To overcome these gaps and comprehensively capture all related facets pertaining to the nature and diversity of invasion impact, this scoping review of academic studies, grey literature, and expert reports provides a conceptual model for interpreting invasion impacts, structured around three interrelated pillars: impact domains, challenges in the study of impacts, and available risk- and impact assessments. We initially explore the various mechanisms and consequences of ecological, economic, and socio-cultural invasion impacts and their temporal dynamics, substantiating these with relevant empirical examples. We then review common challenges and fallacies in studying invasion impacts, including context specificity and inter-comparability of impact magnitudes, challenges associated with quantifying non-ecological impacts, and research biases, before synthesising how risks are analysed and impacts assessed, and how these assessments ultimately inform management decisions. Our review underscores the multifaceted and complex nature of invasion impacts, and that effectively addressing biological invasions requires more than isolated, reactive interventions; it calls for globally coordinated, proactive action underpinned by reliable scientific knowledge, sincere political commitment, and broad public engagement. Drawing on nearly a century of literature and global expert contributions, this work offers a comprehensive, nuanced, and timely overview of the potential consequences of biological invasions, providing a valuable foundation for informing future research directions, management interventions, and policy development.