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Studies of the categorical perception (CP) of sensory continua have a long and rich history in psychophysics. A major development was Macmillan et al.'s application in 1977 of signal detection theory to analyze several experimental paradigms, in particular explicating the relation between the psychometric labeling function and discrimination measures. Simultaneously, Anderson et al. proposed a neural model for what we will term synthetic CP, yet this line of research has been less well explored. In this paper, we assess neural-network models of CP with particular reference to their ability to predict the psychophysical behavior of real observers -- including the relation between labeling and discrimination. Synthetic categorization of a variety of stimuli, including speech sounds and artificial/novel dimensions, is reviewed and discussed in terms of both classical theories of CP and more recent developments. A variety of neural mechanisms is capable of replicating the essentials of categorical perception, indicating that CP is not a special mode of perception but an emergent property of any sufficiently-powerful general learning system. However, the most convincing replication is from a simulation whose output is continuous rather than discrete.