In this paper, we build upon Bruno Latour’s political writings to address the current impasse regarding algorithms in public life. We assert that the increasing difficulties at governing algorithms—be they qualified as “machine learning,” “big data,” or “artificial intelligence”—can be related to their current ontological thinness: deriving from constricted views on theoretical practices, algorithms’ standard definition as problem-solving computerized methods provides poor grips for affective dissensions. We then emphasize on the role historical and ethnographic studies of algorithms can potentially play in the politicization of algorithms. By both digging into the genealogy of algorithms’ constricted definition and by making their contemporary constitutive relationships more visible, both historical and ethnographic studies can contribute to vascularizing algorithms and making them objects of enlarged disputes. We conclude by giving a flavor of the political potential of the vascularization efforts we call for, using materials from an ethnographic study conducted in a computer science laboratory.