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In the present paper we provide an up-to-date overview of nonparametric Cumulative Sum (CUSUM) monitoring schemes. Due to their nonparametric nature, such memory-type schemes are proved to be very useful for monitoring industrial processes, where the output does not match to a particular distributional model. Several fundamental contributions on the topic are mentioned, while recent advances are also presented in some detail. In addition, some practical applications of the nonparametric CUSUM-type control charts are highlighted, in order to emphasize their crucial role in the contemporary online Statistical Process Control.