Current online moderation follows a one-size-fits-all approach, where each intervention is applied in the same way to all users. This naïve approach is challenged by established socio-behavioral theories and by recent empirical results that showed the limited effectiveness of such interventions. We propose a paradigm-shift in online moderation by moving towards a personalized and user-centered approach. Our multidisciplinary vision combines state-of-the-art theories and practices in diverse fields such as computer science, sociology and psychology, to design personalized moderation interventions (PMIs). In outlining the path leading to the next-generation of moderation interventions, we also discuss the most prominent challenges introduced by such a disruptive change.