Experimentalists tend to classify models of visual perception as being either local or global, and involving either feedforward or feedback processing. We argue that these distinctions are not as helpful as they might appear, and we illustrate these issues by analyzing models of visual crowding as an example. Recent studies have argued that crowding cannot be explained by purely local processing, but that instead, global factors such as perceptual grouping are crucial. Theories of perceptual grouping, in turn, often invoke feedback connections as a way to account for their global properties. We examined three types of crowding models that are representative of global processing models, and two of which employ feedback processing: a model based on Fourier filtering, a feedback neural network, and a specific feedback neural architecture that explicitly models perceptual grouping. Simulations demonstrate that crucial empirical findings are not accounted for by any of the models. We conclude that empirical investigations that reject a local or feedforward architecture offer almost no constraints for model construction, as there are an uncountable number of global and feedback systems. We propose that the identification of a system as being local or global and feedforward or feedback is less important than the identification of a system's computational details. Only the latter information can provide constraints on model development and promote quantitative explanations of complex phenomena.