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The spreading of digital technology has resulted in a dramatic increase in the demand for data compression (DC) methods. At the same time, the appearance of highly integrated elements has made more and more com- plicated algorithms feasible. It is in the fields of speech and image trans- mission and the transmission and storage of biological signals (e.g., ECG, Body Surface Mapping) where the demand for DC algorithms is greatest. There is, however, a substantial gap between the theory and the practice of DC: an essentially nonconstructive information theoretical attitude and the attractive mathematics of source coding theory are contrasted with a mixture of ad hoc engineering methods. The classical Shannonian infor- mation theory is fundamentally different from the world of practical pro- cedures. Theory places great emphasis on block-coding while practice is overwhelmingly dominated by theoretically intractable, mostly differential- predictive coding (DPC), algorithms. A dialogue between theory and practice has been hindered by two pro- foundly different conceptions of a data source: practice, mostly because of speech compression considerations, favors non stationary models, while the theory deals mostly with stationary ones.