Since its inception in 1992, the fuzzy ARTMAP (FAM) neural network (NN) has attracted researchers' attention as a fast, accurate, off and online pattern classifier. Since then, many studies have explored different issues concerning FAM optimization, training and evaluation, e.g., model sensitivity to parameters, ordering strategy for the presentation of the training patterns, training method and method of predicting the classification accuracy. Other studies have suggested variants to FAM to improve its generalization capability or overcome the prime limitation of the model, which is category proliferation (i.e., model complexity that increases with data complexity). Category proliferation is pronounced in problems that are noisy or contain a large degree of class statistical overlapping. In many investigations, FAM was improved by incorporating elements of optimization theory, Bayes' decision theory, evolutionary learning, and cluster analysis. Due to its appealing characteristics, FAM and its variants have been applied extensively and successfully to real-world classification problems. Numerous applications were reported in, for example, the processing of signals from different sources, images, speech, and text; recognition of speakers, image objects, handwritten, and genetic abnormalities; and medical and fault diagnoses. When compared to other state-of-the-art machine learning classifiers, FAM and its variants showed superior speed and ease of training, and in most cases they delivered comparable classification accuracy.