This contribution aims at proposing a framework for articulating different kinds of “normativities” that are and can be attributed to “algorithmic systems.” The technical normativity manifests itself through the lineage of technical objects. The norm expresses a technical scheme’s becoming as it mutates through, but also resists, inventions. The genealogy of neural networks shall provide a powerful illustration of this dynamic by engaging with their concrete functioning as well as their unsuspected potentialities. The socio-technical normativity accounts for the manners in which engineers, as actors folded into socio-technical networks, willingly or unwittingly, infuse technical objects with values materialized in the system. Surveillance systems’ design will serve here to instantiate the ongoing mediation through which algorithmic systems are endowed with specific capacities. The behavioral normativity is the normative activity, in which both organic and mechanical behaviors are actively participating, undoing the identification of machines with “norm following,” and organisms with “norminstitution”. This proposition productively accounts for the singularity of machine learning algorithms, explored here through the case of recommender systems. The paper will provide substantial discussions of the notions of “normative” by cutting across history and philosophy of science, legal, and critical theory, as well as “algorithmics,” and by confronting our studies led in engineering laboratories with critical algorithm studies.