Biological invasions, resulting from human activities, exert substantial impacts on ecosystems worldwide. This review focuses on marine invasive alien species (IAS) in Europe, examining the current state, proposing strategies to address the problem, and offering recommendations for enhanced management. Effective management of biological invasions relies on accessible, accurate data to inform decision-making. Information systems such as the European Alien Species Information Network (EASIN), Aquatic Non-Indigenous and Cryptogenic Species (AquaNIS), and World Register of Introduced Marine Species (WriMS) provide comprehensive databases on IAS, but their sustainability requires long-term maintenance, continuous updates, and support. Most countries lack specific monitoring programs for marine IAS, and standardization and improvement of monitoring methods are needed. Port monitoring plays a vital role in the early detection of new arrivals, and recent advancements in molecular techniques show promise for effective IAS monitoring. Risk screening tools are commonly employed to rank taxa based on their invasiveness potential in European regions, but variations in protocols can yield inconsistent results. European impact assessments highlight resource competition, novel habitat creation, and predation as primary mechanisms for negative impacts on biodiversity, while the creation of novel habitats represents a key mechanism for positive impacts. Preventing IAS introductions is critical, and measures such as ballast water treatment systems are implemented to reduce the likelihood of marine introductions. However, understanding introduction pathways remains uncertain for many IAS. Eradication and control efforts for marine IAS have limited success, emphasizing the need for enhanced biosecurity measures. Climate change, especially ocean warming, can intensify IAS impacts on native species and ecosystems. In climate change hotspots, some tropical aliens may, however, compensate for the loss of thermally sensitive natives with similar traits. Therefore, it is imperative to consider the interactions between climate change and IAS in developing effective management and conservation strategies. Enhancing IAS management in Europe entails i) securing adequate funding, ii) expanding the list of IAS of Union Concern to adequately cover marine invasions, iii) learning from countries with successful biosecurity practices, iv) sustaining information systems, v) improving monitoring and early warning systems with innovative technologies, vi) enhancing prediction models, vii) conducting integrated impact assessments and mapping cumulative IAS impacts, and vii) considering the potential benefits of IAS in ecosystem functioning and services.