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Abstract Functional networks (FNs) are extensions of neural networks (NNs). Unlike NNs, FNs considers general functional models instead of sigmoid-like models. Additionally, in FNs, there are no weights associated with the links that connect neurons. In this paper, we review the research progress and applications of FNs models in recent years. First, we introduce FNs architecture, three typical functional models and the learning process, and we explain the differences between NNs and FNs. Second, we discuss recent applications of FNs that have been introduced in many fields, such as time series prediction, differential and functional equations, pattern classification, detection and prediction, approximation computation, complex system modeling, computer-aided design (CAD), and linear and nonlinear regression. Finally, we present some remarks on future research directions for FNs. [ABSTRACT FROM AUTHOR]