The aim of this paper is to grasp the relevant distinctions between various ways in which models and simulations in Artificial Intelligence (AI) relate to cognitive phenomena. In order to get a systematic picture, a taxonomy is developed that is based on the coordinates of formal versus material analogies and theory-guided versus pre-theoretic models in science. These distinctions have parallels in the computational versus mimetic aspects and in analytic versus exploratory types of computer simulation. The proposed taxonomy cuts across the (...) traditional dichotomies between symbolic and embodied AI, general intelligence and symbol and intelligence and cognitive simulation and human/non-human-like AI. -/- According to the taxonomy proposed here, one can distinguish between four distinct general approaches that figured prominently in early and classical AI, and that have partly developed into distinct research programs: first, phenomenal simulations (e.g., Turing’s “imitation game”); second, simulations that explore general-level formal isomorphisms in pursuit of a general theory of intelligence (e.g., logic-based AI); third, simulations as exploratory material models that serve to develop theoretical accounts of cognitive processes (e.g., Marr’s stages of visual processing and classical connectionism); and fourth, simulations as strictly formal models of a theory of computation that postulates cognitive processes to be isomorphic with computational processes (strong symbolic AI). -/- In continuation of pragmatic views of the modes of modeling and simulating world affairs, this taxonomy of approaches to modeling in AI helps to elucidate how available computational concepts and simulational resources contribute to the modes of representation and theory development in AI research—and what made that research program uniquely dependent on them. (shrink)