In this article we will consider monstrosity as a political category from a biopolitical perspective. According to the most prominent thinkers on biopolitics, we can understand monstrosity as an objective of biopower that aims to control and eliminate it (Agamben, Esposito), or as a subjectivity that resists appropriation by biopower and create life in common (Hardt & Negri), and produce powerful ways of life (Haraway, Braidotti). We will analyze these two orientations about monstrosity and its relation with the power, through the expressions: 'Politics over monstrosity' -the subjectivities that are constituted as monsters by the biopower- and 'Politics of monstrosity' -the capacity of some subjectivities to confront the biopower and create...