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Researchers have classically addressed the problem of universal compression using two approaches. The first approach has been to develop adaptive compression algorithms, where the system changes its behaviour during the compression to fit the encoding situation of the given data. The second approach has been to use the composition of multiple compression algorithms. Recently, however, a third approach has been adopted by researchers in order to develop compression systems: the application of computational intelligence paradigms. This has shown remarkable results in the data compression domain improving the decision making process and outperforming conventional systems of data compression. This paper reviews some of the previous attempts to address the universal compression problem within conventional and computational intelligence techniques.