Perceiving objects activates the representation of their affordances. For example, experiments on compatibility effects showed that categorizing objects by producing certain handgrips (power or precision) is faster if the requested responses are compatible with the affordance elicited by the size of objects (e.g., small or large). The article presents a neural-network architecture that provides a general framework to account for compatibility effects. The model was designed with a methodological approach ("computational embodied neuroscience") that aims to provide increasingly general accounts of brain and behavior (4 sources of constraints are used: neuroscientific data, behavioral data, embodied systems, reproduction of learning processes). The model is based on 4 principles of brain organization that we claim underlie most compatibility effects. First, visual perception and action are organized in the brain along a dorsal neural pathway encoding affordances and a ventral pathway encoding goals. Second, the prefrontal cortex within the ventral pathway gives a top-down bias to action selection by integrating information on stimuli, context, and goals. Third, reaction times depend on dynamic neural competitions for action selection that integrate bottom-up and top-down information. The congruence or incongruence between affordances and goals explains the different reaction times found in the experiments. Fourth, as words trigger internal simulations of their referents, they can cause compatibility effects as objects do. We validated the model by reproducing and explaining 3 types of compatibility effects and showed its heuristic power by producing 2 testable predictions. We also assessed the explicative power of the model by comparing it with related models and showed how it can be extended to account for other compatibility effects. (Contains 17 figures and 2 tables.)