[From the Introduction] Knowledge can be defined as the capacity of a system to bridge momentary perceptions and older experiences. While in most of mainstream epistemology knowledge is considered a static propositional quality, in (radical) constructivism (RC), knowledge is characterized as dynamic: the basic tenet of constructivism is the idea that mental structures such as cognition and perception are actively built by one’s mind rather than passively acquired. Radical constructivism tries to avoid the dualistic position according to which constructed mental structures gradually adapt to the structures of the real world, and skeptically rejects that the structures of the real world can be compared with mental ones, independently of the senses through which the mental structures were constructed in the first place. In RC, therefore, concepts such as “truth” are relative to a set of antecedent experiences or statements rather than absolute in the sense of matching an objective reality. In mainstream philosophy, knowledge is defined as justified true beliefs (JTB), i.e., all those beliefs a person holds that are true in an absolute sense and that can be justified. This traditional perspective (and its subsequent extensions) suffers from the problem that its three components do not seem to be sufficient to account for knowledge, as demonstrated by Edmund Gettier (1963) and others who further extended Gettier’s original counter examples. In contrast, RC emphasizes that knowledge is a circular yet non-tautological quality that arises in the ongoing dynamics of cognitive processes. Since RC suggests that the cognitive system is organizationally closed, the chain of cognitive processes determines which perceptual content is transformed into experiential elements. Knowledge arises from situated cognitive processes whose dynamics is merely modulated by their environment on the request of the cognitive apparatus rather than by being instructed by it. As a result, knowledge is a relational dynamical structure and does not consist of propositions that could be referentially justified with an outside reality according to the conventional JTB definition of knowledge (Riegler 2007). In this report, some important conceptual and computational constructivist models of knowledge and its dynamics are reviewed, ranging from precursors such as Ernst Mach and Jean Piaget to contemporary computer models.