There are two competing theories of facial expression recognition. Some researchers have suggested that it is an example of “categorical perception.” In this view, expression categories are considered to be discrete entities with sharp boundaries, and discrimination of nearby pairs of expressive faces is enhanced near those boundaries. Other researchers, however, suggest that facial expression perception is more graded and that facial expressions are best thought of as points in a continuous, low-dimensional space, where, for instance, “surprise” expressions lie between “happiness” and “fear” expressions due to their perceptual similarity. In this article, we show that a simple yet biologically plausible neural network model, trained to classify facial expressions into six basic emotions, predicts data used to support both of these theories. Without any parameter tuning, the model matches a variety of psychological data on categorization, similarity, reaction times, discrimination, and recognition difficulty, both qualitatively and quantitatively. We thus explain many of the seemingly complex psychological phenomena related to facial expression perception as natural consequences of the tasks' implementations in the brain.