For mitigation of the effects of pollution, the media, policy makers and, in turn, the scientific community and industry each provide contributions through development of a sense of urgency, and with guidelines and solutions. For non-indigenous species (NIS) that can frequently have negative impacts on the native biota, this is often conveyed in an emotive way to the general public, who are typically keen to help and to get personally involved. This might be through organization of cleaning campaigns, influence on the media, or collaboration with scientists, to inform them of the local presence and abundance of NIS. Alternatively, they might proactively develop technological solutions themselves. To assess the current state of affairs, we reviewed the presence and effects of NIS in the Mediterranean Sea. As so often, any well-planned and successful activity is directly linked to financing, or a lack thereof, and this leads to sometimes untargeted and sporadic measures that are developed within a project or over a limited timeframe, without any sustainability measures. Therefore, we also assessed the activities and strategies that have been financed in this area of NIS mitigation. Based on this review of the presence and impact of NIS, and previous and ongoing activities, we propose a new paradigm to mitigate such pollution: the 8Rs model (i.e., Recognize, Reduce, Replace, Reuse, Recycle, Recover/Restore, Remove, and Regulate). This model extends from the more traditional 3Rs model (i.e., Reduce, Reuse, and Recycle) that is often used and promoted for innovative waste management strategies. Importantly, the 8Rs model can be applied sequentially, for either prevention of NIS introduction, or preparation of mitigation measures. The 8Rs model was constructed based on Mediterranean NIS, although we believe it can be applied to other sources of pollution and other geographic areas. Importantly, the 8Rs model represents a general framework to organize and categorize future pollution mitigation strategies. This approach is essential for development of any action plan to influence the administrative and financial decision makers who essentially enable these activities, and therefore who have important roles in the guarantee of sustainability of these actions, and the creation of innovative societies.