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This paper traces the development of neural-network (NN)-based feedback controllers that are derived from the principle of adaptive/approximate dynamic programming (ADP) and discusses their closed-loop stability. Different versions of NN structures in the literature, which embed mathematical mappings related to solutions of the ADP-formulated problems called ldquoadaptive criticsrdquo or ldquoaction-criticrdquo networks, are discussed. Distinction between the two classes of ADP applications is pointed out. Furthermore, papers in ldquomodel-freerdquo development and model-based neurocontrollers are reviewed in terms of their contributions to stability issues. Recent literature suggests that work in ADP-based feedback controllers with assured stability is growing in diverse forms.