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A data string can be represented with the help of context-free grammar such that the string is the unique string belonging to the language of the grammar. One can then losslessly compress the string indirectly by encoding the grammar into a unique binary codeword. This approach to data compression, called grammar-based data compression, can also be employed to losslessly compress graphical data structures, which are graphs in which every vertex carries a data label. Under mild restrictions, grammar-based data compression schemes are universal compressors, meaning that they perform at least as well as any finite-state compression scheme. Some of the theory of universal grammar-based compressors is surveyed. Applications of grammar-based compressors to various areas, such as bioinformatics and data networks, are discussed. Future directions for grammar-based compression research are outlined, including compression issues arising in highly repetitive databases and issues concerning the compression of sparse graphical data.