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The Shuffled Complex Evolution (SCE-UA) method developed at the University of Arizona is a global optimization algorithm, initially developed by Duan et al. [Duan, Q., Sorooshian, S., and Gupta, V. "Effective and efficient global optimization for conceptual rainfall-runoff models", Water Resources Research, 28(4), pp. 1015-1031 (1992)]. for the calibration of Conceptual Rainfall-Runoff (CRR) models. SCE-UA searches for the global optimum of a function by evolving clusters of samples drawn from the parameter space, via a systematic competitive evolutionary process. Being a general-purpose global optimization algorithm, it has found widespread applications across a diverse range of science and engineering fields. Here, we recount the history of the development of the SCE-UA algorithm and its later advancements. We also present a survey of illustrative applications of the SCE-UA algorithm and discuss its extensions to multi-objective problems and to uncertainty assessment. Finally, we suggest potential directions for future investigation. (C) 2019 Sharif University of Technology. All rights reserved.